Can predictive models make predictions for individuals or only for groups? I am an MBA Student taking courses in statistics.
In this last week, I have heard two conflicting opinions from my professors on Statistics.

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*1) Predictive Models can NOT make predictions on individuals - only on groups: My professor from my "Research Methods" class introduced us to the concept of the "Ecological Fallacy" (https://en.wikipedia.org/wiki/Ecological_fallacy). He pointed out that very often, the behavior of individuals within a group will not be similar to the average behavior of the group. He mentioned that statistical models can ONLY be used to describe variations within groups - he mentioned the importance of concepts such as "Propensity Score Matching" and correctly designing experiments while accounting for possible inconsistencies.


*He mentioned that if a pharmaceutical drug was found to be effective on a cohort of men all having similar age groups, lifestyles, backgrounds and medical histories - the best we can do is say that any man from the general public who fits this cohort profile will likely experience similar effects from this drug : we can not really make any individual prediction apart from this.


*He mentioned the field of "Survival Analysis" and told us that statistical models are routinely used to estimate the survival odds and hazard of surviving at the group level and not the individual level - he gave us an example: if you have 1 Male Asian Patient and 99 Male Non-Asian patient, you have no choice but to analyze the average survival rates of MALES ... how can you perform "Asian Specific Analysis" and make inferences about the average Asian when you only have 1 observation!?


*He closed by mentioning the new and emerging field of "Precision Medicine" in which "accurate molecular taxonomy of diseases that enhances diagnosis and treatment and tailors
disease management to the individual characteristics of each patient " (https://www.mdpi.com/2227-9717/10/6/1200/pdf) - i.e. for the first time, medical treatments are being considered for the individual patient's condition, and not for the average profile of this patient (although he mentioned that this is still in its infancy and should be used with great caution).


*With this, he largely dismissed "Data Science" as a "pseudo science" and said although many "Data Science" models have demonstrated success, the methodology is not mathematically rigorous and can only be considered as an "engineered solution" (e.g. a Random Forest predicting if an individual patient will develop a disease - he said that this should not be done for many reasons, e.g. interpretability, blackbox, lack of odd's ratio and individual prediction).


*He closed with this final example : Imagine two bridges. The first bridge can only support a load of 100 kilograms, but has been rigorously tested in theory (e.g. physics, material science) and empirically - the reputation and behavior of this bridge has been well documented and observed under various conditions. The second bridge has been demonstrated to support loads of up to 500 kilograms, but we have no idea how this bridge was built or whether it will collapse in the future when subject to even 50 kilograms. He asked us - which bridge are you more confident walking across? He said this in a rhetorical tone, and said obviously the first bridge that has demonstrated both theoretical and empirical success should be favored over the second bridge - even if the first bridge is believed to be less stronger than the second bridge. He quipped that the first bridge is Classical Statistics and the second bridge is Data Science. He told us that perhaps this example is an extreme example, but this is precisely why a drug that has initially shown strong potential for curing a disease must be rigorously studied in both theoretical and empirical settings before it can be released - and in the interim, potentially less effective but better understood drugs must be administered of which we have higher confidence in.


*2) Predictive Models CAN be used to make predictions on individuals: On the other hand, my Data Science professor thinks otherwise. I told him the views of my "Research Methods" professor and he stated that research publications would suggest otherwise. He showed me publications (e.g. https://www.sciencedirect.com/science/article/pii/S2666827021000694, https://pubs.rsna.org/doi/full/10.1148/radiol.2018180547) in which predictive models have indeed demonstrated success in making individualized predictions - for example, successfully predicting the presence of COVID-19 in individual patients. He basically said that he sees no reason as to why Predictive Models can not be used for individual prediction - and if the  opposite was true, he would have been long out of a job.
This has left me conflicted - I find myself agreeing with the opinions and views of both professors at the same time.
Can someone here provide some insights to bridge these two views together?

Of course you can use predictive models on individuals. They wouldn't be very useful if you couldn't.
Your statistics professor's position is so bizarre that I wonder if maybe something got lost in communication.  For example, if we were to take your reporting of his comments at face value, we would have to conclude that he had never heard of prediction intervals, which seems unlikely for a professor of statistics.
Formally, a statistical model model predicts a probability distribution for the random variable $Y$ that it is modeling.  For example, an ordinary least squares model predicts:
$$Y_i \sim \text{Normal}(\alpha + \beta x_i, \sigma),$$
where $\sim$ means "is distributed as".  The $\alpha$, $\beta$, and $\sigma$ are all parameters of the model; finding them is what we mean by "fitting" the model.  So, it's baked into the definition of the model that we can't predict an individual case with certainty.
When people talk about the model "predicting" $\hat{y}_i$ for a case, they usually mean that $\hat{y}_i$ is the expected value of the predicted distribution.  Depending on the circumstances that may or may not be a useful summary of the model's predictions, but it's not the whole story.  For example, if you care about individual variation, you might compute a 95% prediction interval as $\hat{y}_i \pm 2\sigma$, which gives an idea of the range of actual events you might commonly encounter.  Note, by the way, that this prediction interval will generally be much larger than a "confidence interval" for $\hat{y}_i$.  The confidence interval tells you about the uncertainty in the estimate of the expectation value, which is something that is only relevant to populations.
Now, machine learning practitioners often elide all of this and just talk about "the prediction" of the model.  Depending on what those are trying to do, this might be a reasonable approach, or it might not.  Sometimes you need a system that is going to take its best guess and move on; it all depends on what you are trying to accomplish.  I happen to think that ML models should make probabilistic predictions more often than they do, so perhaps some criticism of data science is due there, but a blanket dismissal dramatically overstates the case.
Most of your professor's other criticisms seem like red herrings to me.  Obviously a model fit to data from a very limited population is only useful within that population.  This comes as a surprise to nobody.  And I can't even figure out what he's trying to say with his bridge analogy.
One thing I think we can all agree on is this:  it's good to give some thoughts to what your model's predictions actually mean and what their limitations are.  It's fair to be skeptical of boiling a prediction down to a single number, as long as you recognize that sometimes that is the right solution for certain problems.  The best way to use a statistical model is to think about what question you are trying to model, and consider all of the information returned by the model and how it might be used to answer that question.  That last part demands judgement, and developing and exercising good judgement is where data scientists and statisticians alike earn their keep.
