I probably wasn't very clear. Let me try again.
People are looking at, "what is probability of 6 heads?" as if that is the only possible question. It isn't the only possible question.
If you are only talking about probability of 6 heads, I don't disagree at all.
But if instead of asking, what is the probability we ask, "how unusual is it to get 6 heads in a row?" it is a different question. And the answer is, it's not unusual at all.
One is theoretical probability, which cannot be applied to the realty of 6 actual coin tosses. You will not get 3 heads and 3 tails every time. Because probability explains the odds of large samples.
Toss a coin 100 times and record the result. Is it unusual (or odd) to get 6 heads in a row among those 100 coin tosses? I will assume we agree it would not be unusual.
Given that a run of 6 is not unusual in a 100 coin toss, is it more or less likely that run of 6 will happen with the first 6 tosses than somewhere in the middle? There is nothing inherent in the coin toss that says you have to toss the coin more than six times to get 6 heads in a row.
Every coin toss has a 50:50 chance of heads or tails.
If you forget about heads and tails for a minute and assign each combination a name. Of your 64 names what is the probability of any one name coming up?
Or try this, if you toss a coin and you get 5 heads in a row, are you now more likely to get tails in the next toss?
Probability is one thing. And we agree on the probability of 6 heads in 6 tosses. So what then explains the fact one gets less probable outcomes? Unless you are talking about a huge number of tosses, the probability of getting 6 heads isn't useful. Especially not in this case.
It doesn't mean I don't agree with you. It means I think one can look at the probability differently than just the probability of 6 heads.
Given there are 64 different possible combinations (remember this is 6 coin tosses here, not 6,000 tosses) it's more useful to consider each of those combinations has an equal chance of occurring.