No. This is wrong. The correct form is "..look forward to seeing". As Beth has explained, the "to" is a preposition - part of the phrasal verb "look forward to" - and is not part of an infinitive construction. The common mistake is to presume that "to" must always be followed by an infinitive. I have come across near-bilingual non-native speakers who still make the mistake of saying "look forward to see". As for your teacher, there are two possibilities: 1. He is lying about being a native speaker (a sadly common occurrence). 2. He is over-applying a rule that he doesn't quite understand. Unfortunately, this can also happen, especially among under-qualified native speakers who teach abroad. Either way, he is not to be trusted, and you may want to consider finding a better teacher.

It is incorrect because 'to' here is just a preposition and has nothing to do with infinitives. I have been speaking and listening to English all my life and I have never once said or heard said ' I look forward to see you' The only way 'I am looking forward to see you' would be correct if I was talking about the physical direction, for example ' You are standing infront of me, so yes then, I look forward to see you, because if I look to the right, left or back, I can't see you.

See Beth's answer. :)

i think it is correct, Looking forward to seeing you soon