Would you consider this "pushing someone away"

So I've been with my boyfriend for almost 3 years. He hasn't had the best past so when we first started dating he hated talking about his family life and would hold it all in. Eventually he would come to me to vent and he started being more open about stuff and now it normal. Everything was fine. About 3 months ago things started get rocky in our relationship and I felt like things were different i found out he was cheating on me. I forgave him and tried to move past it. Than something else happened and things aren't getting better. We are trying to work past it he claims he is trying to fix his mistakes and that he loves me so much. I told him he was pushing me away. He said he wasn't and I told him all the lies he told me were pushing me away and he stopped coming to me with his issues. Basically my question is, do you thing your s/o telling you lies and acting different considered pushing you away ?