A language is regular only if some finite automaton recognizes it. The pumping lemma is theory of computation's first impossibility proof — the way to show a language is not regular.
Suppose a DFA with p states accepts a string of length ≥ p. Reading it visits p+1 states, so by the pigeonhole principle one state must recur — the path closes a loop. Split the string w = x y z around that loop (with |xy| ≤ p, |y| ≥ 1). Because the loop returns to the same state, the machine ends in the same place no matter how many times you go around: x yⁱ z is accepted for every i ≥ 0.
For aⁿbⁿ the Demon's finite counter can only track a's modulo p, so pumping the a-loop makes aⁿ⁺ᵏᵖ bⁿ — still accepted, but with too many a's to be in the language. One accepted string outside L breaks the claim: aⁿbⁿ is not regular. Try the same attack on (ab)ⁿ, which truly is regular, and it fails — the loop reads "ab", so pumping only builds more (ab)ⁿ. A working attack is a disproof; a failing one is honest.
The simulation stopped unexpectedly — the lesson continues without it. You can move on; nothing you did was wrong.