“That one doesn't count!”

You're at a bar with your friend, and the conversation turns to car accidents. You and your friend have both had a lot of accidents, and you start to compare who has been in more. Your friend lists a small accident that he had where he hit a mailbox in front of his house. You don't think that should be accepted in the comparison because it was too small of an accident. You say:

That one doesn't count!

that one

Use "that one" to refer to an example that someone gave earlier in the conversation.

To refer to an example that you are going to give, use "this one":

Oh you think that's good? Listen to this one!

You would then give your example.

(something) doesn't count

Use this when you're counting or comparing things (like the number of accidents you've had), and one of the items doesn't fit the category. Here's another example:

Golf doesn't count as a sport. It's too slow.