{Animar, Soul of Elements} on the field and has 10 counters on it. I cast a {Savageborn Hydra} for RG. The hydra comes in as a 10\10. My buddy said that I have to have other mana to pay for X. Is that true? I don't think so but just wanted to make sure...
Your friend is wrong, as llama stated. When you cast a spell with X in its casting cost, you choose a value for X, and then calculate costs.
In this case, hydra reads {1}{0}{R}{G}. Then Animar says: I'll give you {1}{0} discount, so it costs only {R}{G}, yet still comes into play with the X you chose for it: 10.
That's what I thought, thanks for the clarification!