Relationship advice?

TL;DR: my boyfriend of nearly a year won’t go out in public with me even when I ask

My boyfriend and I have been together for about 11 months now. Things are great when we’re over at his house, but he will not go in the public with me! We’ve never gone out to dinner (I’ve offered many times, offering to pay for it and everything) he won’t go. He won’t go to the store with me when I ask. He didn’t tell his family about me for a very long time. We were hosting thanksgiving at his house for his family, whom I am had never met. It was around month 8 of dating. This was planned at least a month in advance, and I found out on thanksgiving day about an hour before everyone arrived that he had not told them that I existed until just then. I have expressed over and over again that I don’t like that he is never seen in public with me, that I am frustrated and I feel like he’s embarrassed of me or something. He always just says sorry and that I’m important to him, but nothing changes. I also recently brought it up to him that he never asks me to come over, I’m always the one to ask. He said that it should be implied that he wants me over 🙄. I told him that wasn’t good enough. I really care for him, but this is seriously getting to me. I told myself after I left his house the last time that I will not go over there until he asks me next time. It’s been over a week of waiting. I find myself daydreaming of dating someone that will take me out in public..but I’d really like to make this work