to meeting vs. to meet

Here is a familiar problem.

I was asked to help with the phrases:

"I'm looking forward to meeting you. vs. I'm looking forward to meet you".

Correct is: I'm looking forward to meeting you.

Why?
The verb is in this sentence is 'to look forward to' which also means 'to anticipate'. These are transitive verbs which require a direct object.

In the example “I'm looking forward to meeting you” the direct object is a gerund. A gerund is a noun form of the verb 'to meet’.

In contrast in the sentence “I'm waiting to meet you” ‘to meet’ is the infinitive.

There are some verbs that are followed by a gerund and some that are followed by an infinitive. And then there are some that are followed by either a gerund or an infinitive.

You simply have to memorize these verbs.