That's a fair critique, but most people (that I've spoken to about this anyway) understand that a rocket needs to "push against gravity" to go places, they just forget or don't know that orbital velocity is a thing and what it means (or that you need to cancel that orbital velocity out before you can start using gravity, and that gravity is ultimately pretty weak)
The analogy is meant to try and explain why going toward the sun might be harder, especially when it is so counter-intuitive if you've never thought about it, and it does so by taking some liberties with parts of orbital mechanics that people already instinctively understand.
I think on balance it's a definitely a decent analogy, this was just something that jumped out at me as being a possible source of confusion. If this is an analogy that you've used successfully without this confusion coming up then it's probably not too big a deal.
The analogy is meant to try and explain why going toward the sun might be harder, especially when it is so counter-intuitive if you've never thought about it, and it does so by taking some liberties with parts of orbital mechanics that people already instinctively understand.