Because drinking isn't dangerous, and driving isn't dangerous – at least, not in comparison to the single activity "drinking and driving" – the two words are treated as a single unit.
This might happen a lot when we combine two or more elements in a sentence:
My favorite drinks are gin and tonic.
This could mean I have two favorite drinks: gin is a favorite drink, and so is tonic.
My favorite drink is gin and tonic.
This means that a gin-and-tonic is my favorite drink.
ell.stackexchange.com/users/113/J.R.
There, and is understood to mean "in combination with" hence the singular is appropriate.
They are not individually dangerous
(if you don't drive recklessly and drink in moderation) and that's why you wouldn't say are .
ell.stackexchange.com/users/10264/Tᴚoɯɐuo
If you say: Drinking and driving are dangerous.
this is the equivalent of saying: Drinking is dangerous.
Driving is dangerous.
By saying: Drinking and driving is dangerous.
we mean that drinking to the state of being intoxicated, even mildly, and then driving while still intoxicated, is dangerous.
However, the quote is much pithier than the explanation!
ell.stackexchange.com/users/9936/CJ Dennis
The combination of drinking and driving is a single object.
Here we see one combination of two things.
The common phrase 'drinking and driving is dangerous' is leaving out some clarifying words.
"Drinking and driving are dangerous" has a particular meaning:
drinking is dangerous (perhaps) and driving is dangerous (perhaps), if you look at each singularly.
The meaning of your sentence is that [the combination of] drinking and driving is dangerous.
An new example of 'is vs. are' with clearer context may help: Singing and rock climbing are challenging activities.
Singing while rock climbing is a more challenging activity.
ell.stackexchange.com/users/67240/Hbada
In standard English when a list of items is used as the subject of a verb then, that verb takes the plural even if all the items in the list are singular.
For example you would say Gold, iron, copper and aluminium are metals rather than is metals (although some dialect have the opposite convention).
BUT 'drinking and driving' is a list but effectively a single compound noun.
actually 'drunk driving' would be more grammatically correct but has been abandoned as the precise definition of 'drunk' is too ambiguous in this context and the phrase is used to reinforce the idea that drinking any alcohol before driving is dangerous even if you don't think you are 'drunk'.
This is different to saying 'drinking is dangerous, driving is dangerous'.
ell.stackexchange.com/users/32210/Chris Johns
It is the singular act of drinking and driving that is being described as dangerous.
In describing multiple acts that are individually considered to be dangerous you would use the plural form of the verb.
For example: Drinking and driving is dangerous and illegal.
Smoking and mountain climbing are dangerous and legal.
ell.stackexchange.com/users/67293/Andrew
"Drinking and driving" is treated as one unit in this case.
"Drinking and driving" is dangerous "X" is dangerous Interestingly, in the UK
the expression is "drink-driving", and it's still treated as a singular unit and can be placed right into the same structure: "Drink-driving" is dangerous
ell.stackexchange.com/users/67305/David Calhoun
In the sentence: "Drinking and driving is dangerous". Drinking and driving are both subjects and the word dangerous is the object (I think) but why do I have to use the verb to be in singular?
In the sentence: "Drinking and driving IS dangerous", why does the verb "to be" need to be singular?
ell.stackexchange.com
<subject-verb-agreement><compound-subjects>
ell.stackexchange.com/questions/151717
ell.stackexchange.com/users/30184/claudio sepulveda
The combination of drinking and driving is considered to be a single object. The meaning of your sentence is that [the combination of] drinking and driving is dangerous. The combination of drinking and driving is a single object.
The combination of drinking and driving is a single object. Here we see one combination of two things. The common phrase 'drinking and driving is dangerous' is leaving out some clarifying words.  