Why sometimes the verb after "to" is in present continuous tense?
1. In manifesting their opposition to cutting down trees, not everybody expressed their views by providing arguments.
2. Learning to be charitable gets you a long way to becoming a good logical and critical thinker.
3. I look forward to hearing from you.

These are the three examples that I find when the verb after "to" is in present continuous tense. Why? And since many times the verb after "to" is in its orginal form - the present simple tense, how to distinguish them in this case and use the right tense?

Question

Why sometimes the verb after "to" is in present continuous tense?
1. In manifesting their opposition to cutting down trees, not everybody expressed their views by providing arguments.
2. Learning to be charitable gets you a long way to becoming a good logical and critical thinker.
3. I look forward to hearing from you.

These are the three examples that I find when the verb after "to" is in present continuous tense. Why? And since many times the verb after "to" is in its orginal form - the present simple tense, how to distinguish them in this case and use the right tense?

Answer

These sentences are NOT in the present continuous. Please don't make the mistake of thinking that all instances of the 'ing' form involve the present continuous. This has nothing to do with tenses.

In fact, 'cutting', 'becoming' and 'hearing' are all examples of gerunds. Gerunds are verb forms functioning as nouns.

In all of these cases, 'to' is a preposition - like 'with' 'from 'by' and so on - and prepositions are followed by gerunds. I suggest you go back to your grammar book at look up the use of gerunds.

Answer

To add to Su.Ki's comment, "to" is a preposition, which requires a NOUN.  To convert a verb into a noun, its GERUND form (ing) must be used.

Consider:

I like what?  (WHAT = direct object = NOUN).
I like ski.  (NO; "ski" is not a noun form of the verb 'to ski')
I like skiiing.  (YES; gerund is a NOUN)
I like to ski.  (YES; infinitive can also serve as a noun form of a verb.)

Answer

because now to is a prep, not to do.  when to is a prep, we should add ing behind a verb.  for example , pay attention to doing, look forward to doing .