grammaticality - “All you have to do is read” vs. “All you have to do is to read”

I was speaking to an English learner and said, “All you have to do is read a lot.” And they thought that sentence wasn’t grammatically correct because I dropped the word to between is and read.

They thought it should be “All you have to do is to read a lot.” That sounds weird to me.

How do I explain to them the reason you drop the to? Or am I incorrect and it really should have a to?