Your perception is spot on: your boyfriend is afraid of losing you. That anxiety is indeed what makes him clingy. Getting past that anxiety is actually a complicated and messy process, but let’s assume the best and say that your boyfriend is a reasonable sort who is open to changes. In a case like this, the problem is relatively straightforward: he simply doesn’t recognize his behavior as clingy. So you need to explain things until he sees the situation through your eyes. If he’s the decent sort, he will try to modify his behavior.
Just don’t forget to be specific with your boyfriend about explaining what crosses the line between attentiveness and smothering. Of course, that line can shift day to day, so prepare him for that possibility too. And as for yourself, be realistic. Expect to have this same conversation more than once. If your boyfriend is dealing with his own deep seated insecurities, these will be subconscious. And our subconscious has a habit of making us do things even when the conscious mind knows better.
You might find yourself worrying too much about hurting his feelings. Don’t let that stop you. There are ways to take the sting out of this conversation. It never hurts to also use this talk as a way to re-affirm the specific things he is doing right and that you appreciate. Remind him that you bring this matter up only because you already value the relationship and want to make it work better.