What would you do?

My boyfriend constantly lies. He’s cute blatantly deleting text messages, and h uses Facebook to lie as well. We are on the same Verizon plan so you can see who is being called and texted. Since he knows this he uses Facebook messenger to lie. We don’t live together so he constantly goes on Facebook and makes plans to go out drinking with friends. Then tells me he’s going to bed or he has a headache or whatever. I usually find out, but I’m sure there are times I haven’t. All of our fights revolve around him lying and his Facebook usage. I think if he loves me and wants to earn trust back he needs to deactivate Facebook for a while. He thinks it’s my way of controlling him. Am I being fair in asking him to delete it for a while?