You can tell someone “I’m not ready to talk about it” and mean “maybe later,” not “never.”

The fear is that asking for time will be heard as a door closing, so people either talk before they have any idea what they think, or avoid the whole thing until it goes bad. A pause is not a refusal. It does need a small amount of shape, though, because the other person is quietly filling the blank with the worst available version.

Add a few words to the end of it. Not tonight, maybe this weekend. Then come back to it, even briefly, even to say you still are not ready. That second part is what makes the first part believable next time.