Yes it is irrational. That's a common statistical misconception, the key thing here is that every flip has a 60% chance of being heads.
The result of each flip is completely independent of what came before it. In your example the 7th flip is just as likely to be heads as the first flip, or any of the other 5 flips that landed on heads.
The result of each flip is completely independent of what came before it. In your example the 7th flip is just as likely to be heads as the first flip, or any of the other 5 flips that landed on heads.