I'm not a teacher***
To often forms an infinitive, e.g. I want to go to bed. I need to go to the bathroom first though.
However, in your example I look forward to seeing you, to is not part of an infinitive, it's a preposition after which you can either use a noun (e.g. I look forward to your visit) or -ing.
Other expressions that you can use this way are for example:
- be used to
- object to
I'm used to going to bed late.
He objected to having to wait for me for an hour.
Student or Learner