Would you consider this treating someone badly?

Pretend you have a boyfriend. He's clingy and texts you from the time he wakes up till the time you go to sleep at night. If you don't text him back within 5-10 minutes he'll text you again wondering why you haven't texted him back yet. He doesn't really do much, he usually just sits at home all day playing video games or doing stuff on the computer. You've been really busy (which is an excuse he doesn't usually accept for you not texting him, he wants to know every detail of what you were doing that made you not able to text him) and haven't texted him for about four days, let alone anyone else (you usually don't text anyone anyway though, unless they've texted you first). Also, you have some depression and anxiety problems, so you're not always up to talking to people. So he sends you about 20 texts and an email asking why you haven't texted him and he says that his dad thinks you're treating him (your boyfriend) like crap, but he (your boyfriend) "knows you'd never do that." And you wouldn't, on purpose anyway. But with the combination of anxiety and having things to do, you just didn't want to talk to him, or anyone else. So would you consider that, not texting someone for four days, treating someone badly?