If you flip a coin and get heads 10 times in a row what is the probability of tails on the 11th flip explained

I was arguing with my friend about this and we need a mathematician to settle it.

I flipped a coin 10 times and got heads every single time. My friend says "the next flip is MORE likely to be tails because its due."

I said "no, the coin doesnt have memory, its always 50/50."

But then my friend said "if its always 50/50, then the probability of 11 heads in a row is $(0.5)^{11} \approx 0.0005$, which is basically impossible. So if ive already seen 10 heads, the 11th being heads would mean an extremely unlikely event happened, so its more likely to be tails."

Is this reasoning correct?? It feels wrong but I cant explain why mathematically. Something about conditional probability vs absolute probability.

Also: if I HADNT observed the 10 heads, then 11 heads in a row is indeed $(0.5)^{11}$. But since ive already observed 10 heads, the conditional probability $P(\text{11th heads} \mid \text{10 heads})$ is just $0.5$. Is that right?