Sometimes it's better not to look at word usage from a grammar perspective. Instead, we can accept that some phrases are 'fixed', and there's no point worrying about the individual words within them.
The phrase "I look forward to seeing you", from yesterday's lesson, is a good example. There's no point trying to understand why we use "to + ing" in this phrase. Just learn it as a fixed phrase.
Let's take another example. Someone asked me for a grammatical explanation of my use of the word "for" in the sentence below:
One option would be for police officers to visit schools. (taken from this essay)
Here's the answer that I gave the student:
It might be best to learn the whole phrase "one option would be for x to..." without trying to understand it word by word. You could consider this to be a 'fixed phrase'.
In other words, rather than looking at this from a grammar perspective, you could learn it as a vocabulary item. Then, the best way to understand the phrase is to see it used in various different contexts. Here are some examples from a Google search:
- One option would be for national authorities to intervene.
- In order to improve the economy, one option would be for the government to invest in infrastructure.
- One option would be for staff to work more hours.