Your thought process makes perfect sense to me. Like Eaten by Bears pointed out, every fossil is a transitional fossil. Every organism is a transitional organism.
How to explain this to a person who refuses to accept that evolution is a possibility, though, I'm still at a loss, so it's not like you're not understanding anything in these conversations. It's just that the reasons that these people give for disagreement aren't really reasons, they're evasions of rationality.
It's akin to me saying that I've never seen the ocean evaporate and form a cloud, Therefore the theory of the water cycle is pseudoscience! Where are the transitional forms??!!1!
One way to demonstrate the validity of the theory of the water cycle, in order to answer to this sort of claim, is to put a chemical marker in the ocean, and we will find that this chemical marker then shows up in the rain that comes from some clouds later, while it wasn't in the rain earlier.
The same goes for details that we can find in the remains of organisms. By studying the different details that are present, we can make a determination of which organisms an organism came from.
The Selfish Gene by Richard Dawkins goes into some of the mechanisms of evolution, both social and biological. It's helped me to answer both the 'how can animals change' question, as well as the 'how can a good society evolve out of no society' questions.