If were true, then you’d have a 50% chance of the coin being heads 100 times in a row. Or 1000, or a million times in a row. Seems unlikely.
The odds ARE the same on each TOSS but that does not mean that the odds of getting heads on every one of a hundred tosses are the same as the odds of getting heads on one. Toss a coin twice and you have a fifty percent chance on either toss but you only have a twenty five percent chance of both being heads or both tails.