‘Drive somebody to’: Why with infinitive?

Solution 1:

First . . . this is not a rule: Use a gerund whenever "to" is not an infinitive marker.

When to is a preposition, it is followed by a noun or something that functions as one (including a gerund):

look forward to dinner
look forward to the meal
look forward to whatever we're having for dinner
look forward to eating

In drive somebody to ___, to is either a preposition or an infinitive marker, depending on what follows it.

When to is a preposition, drive somebody to ___ is followed by a noun or something that functions as one:

drive somebody to the edge of insanity
drive somebody to the store
drive somebody to wherever he or she needs to go
drive somebody to thinking

When drive is used in its sense of compel, drive somebody ___ is followed by a to-infinitive verb phrase—the to infinitive marker + the base form of the verb + whatever else it might need for completion:

drive somebody to leave
drive somebody to finish dinner
drive somebody to stop smoking

Sometimes you have a choice; you just need to decide what you're trying to say:

Preposition + nominal:
Love has driven men and women to strange extremes.
?Love has driven men and women to acting strangely. (somewhat awkward)
*Love has compelled men and women to acting strangely. (incorrect)

Infinitive marker + bare verb etc.:
Love has driven men and women to act strangely.
Love has compelled men and women to act strangely.