Saying "Infer" When They Mean "Imply"

I’ve noticed this error twice on the radio in the last few days. What is so confusing about imply vs. infer? I imply something when I speak, meaning I suggest it but don’t come right out and say something. You infer something when you listen, meaning you interpret something that I did not come right out and say?
Instead, you get this false-correctness of “What I think you’re trying to infer is….”
Now I suppose that you can infer something from what you heard and then imply it with what you say, but still someone objecting to that should cite your implication and not your inference! Or if they really have a problem with whatever you inferred before you implied what you did, then they should make it clear that they are digging into preceding causes and not just confused about what the words mean