Simple linear regression vs Multiple Linear regression interpretation Suppose we have a multiple linear regression model with two predictors, $X_1$ and $X_2$:
$$Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \epsilon.$$
We can interpret $\beta_1$ as the expected increase in $Y$ with a unit increase in $X_1$ when $X_2$ is held constant. This is because $\beta_1$ is the partial derivative of the expected value of $Y$ with respect to $X_1$.
Further, suppose that we also compute the simple linear regression of $Y$ against $X_1$:
$$Y = b_0 + b_1X_1 + \epsilon.$$
Then I've seen by some authors that: $b_1$ is the expected increase in $Y$ with a unit increase in $X_1$ without holding $X_2$ constant.
But I really don't see the last point because for me in the simple linear regression is  like holding constant $X_2$ by giving it a zero value.
So why do they say the in the simple linear regression all other predictors not considered are not constant?
I would really appreciate if you can help me clarify this idea.

Try estimating the two models on some dataset:
$$Y = \beta_0 + \beta_1X_1 + \epsilon$$
and
$$Y = \beta_0 + \beta_1X_1 + \beta_2X_2 + \epsilon$$
What you would usually notice is that the $\beta_0$ and $\beta_1$ parameters differ between the two models. In the second you control for $X_2$, in the first one you don't, hence the different parameter estimates. In the first model, by the fact that we didn't include $X_2$, it was accounted for by noise term $\epsilon$. If in the second model you set $X_2=0$ you would consider only the scenario where it is exactly zero. So in fact, in simple linear regression, all the other predictors are accounted for by the random noise, rather than considered constant.
