We use ‘look forward to + gerund’. According to Cambridge the use of gerund is due to the fact that ‘to’ is a preposition when following ‘look forward’ (as opposed to an infinitive marker).
At the same time ‘drive somebody to (+ verb)’ requires the verb to be an infinitive. Cambridge itself gives ‘violent behaviour […] drove her to leave home’ as an example.
Whenever ‘drive somebody to’ is followed by a noun, ‘to’ appears to be a preposition. Cambridge on the same page lists ‘love has driven men and women to strange extremes.’ Collins mentions ‘into’ as an alternative preposition, as in ‘The recession […] drove them into bankruptcy.’
Is ‘to’ in ‘drive somebody to (+ verb)’ a preposition or an infinitive marker?
Assuming ‘to’ is a preposition: If the rule were to use gerund whenever ‘to’ is not an infinitive marker, wouldn’t we need to say ‘drive somebody to + gerund’, as for example ‘violent behaviour drove her to leaving home?’ Wouldn’t that be consistent with ‘look forward to + gerund?’
Long story short: Why is ‘drive somebody to’ followed by an infinitive and not a gerund as e.g. ‘look forward to?’