1. He doesn't reply to your texts.
Wait. Calm down. Let me explain. If you message him in the morning and he replies in the evening, that's because he was looking for the perfect words to reply to you. He was thinking hard about what to say. When he finally replies, you will notice it's a one-word answer, that's because he could not think of anything. However, he didn't want the conversation to end, so he replied your "how are you doing?" with "good".
2. He introduces you to his friends as his sister.
That is because he doesn't want them to get jealous of him, what if they harm him out of jealousy so as to get you. Even Abraham did the same thing to Sarah. He was probably scared to let people know you are the beautiful lady he is dating, so he says you are his sister to protect you and him.
3. He doesn't call you or pick up your calls.
This is easy to understand. He did this because he would stammer, only your voice is enough to intimidate him. He would constantly feel he is not worthy of your love, so he would ignore your calls as he stares at the screen, panicking as your name shows up.
4. He corrects you.
You do not use the word "beat" because he's doing it out of love. He corrects your mistakes so that you can be the perfect woman he wants you to be. You won't find men like this everywhere, hold them tight, they are rare.