Why do we sometimes use the infinitive after "Putea" and other times the subjunctive?
The use of the subjunctive seems a little different from the other romanance languages I have studied. For example here there is no change of subject.
Would it also be correct to say "El nu poate înțeleage"
Minor nitpick: the infinitive is "a înțelege".
And yes, you can say "El nu poate înțelege."
You can even say "El nu poate a înțelege.", although this form is more awkward and belongs rather to a dramatic context than common speech.
The thing is that the subjunctive is just the most common way of expressing this. Whenever a bunch of languages (e.g. English, French) would use the infinitive with verbs like "can", "want", "wish" etc., Romanian would use the subjunctive:
He can eat. - El poate să mănânce.
He wants to eat. - El vrea să mănânce.
He refuses to eat. - El refuză să mănânce.
He decides to eat. - El decide să mănânce.