Hello Laura-Li & welcome.
I think that many parents of 13-year-olds would be uncomfortable with them dating a 16-year-olds, partly, I suppose, because older teenagers are sometime more experienced and expect more from a relationship.
In your case, this would be your first boyfriend, anyway, so I'm just not sure. It depends on the kind of relationship, I suppose. If it's an innocent relationship, it could be fine.
I think that one thing that concerns parents, when it comes to more worldly older teenagers, is if a physical relationship ensues. The age of consent is 16 in England, so some parents would be concerned at over-16s dating under-16s, I think.
I think that, if you get on well with this boy, and his parents are happy with him dating someone older, then why not.
Sorry to be so vague ~ I wonder what others think?
