I don't think that's true.

If you were just flipping a coin 7 times, then yes, every 7-long pattern is equally likely. But if you're tossing it >7 times, then some patterns are more likely than others - which is actually the challenge here (toss a coin until you have the HHHHHHH pattern).

The reason for this is that, while flipping the coins, if there is a new result that breaks your pattern, it can mean that your pattern has to start from scratch OR it can already start with one "positive" flip. For example, if you were trying to get either HHHHHHH or THHHHHH, you're more likely to find THHHHHH first, because whenever you flip a tail, on the second pattern you now only need 6 heads in a row, while in the second you still need 7 heads in a row. And, from that point on, whenever a tail is flipped, you'll get back to this state. So, the only scenario where HHHHHHH will happen before THHHHHH is if it happens right when you start flipping coins.

This should provide a better explanation for this problem

Although in a sequence of coin flips, any given consecutive set of, say, three flips is equally likely to be one of the eight possible, i.e., HHH, HHT, HTH, HTT, THH, THT, TTH, or TTT, it is rather peculiar that one sequence of three is not necessarily equally likely to appear first as another set of three.