FWIW, the first link I provided in post # 24928 above gives you Bob LeVitus opinion on the matter, albeit without explanation. I'll post more if I find something relevant.
Apart from opinions, the main reason
not to run two firewalls in sequence is that both firewalls can have different and conflicting rule sets enabled. In the best case (both with default settings), likely nothing untoward will happen, other than that the software firewall is entirely superfluous, wasting CPU cycles and slowing data passage in the process.
When the issue is
blocking certain access, two firewalls may duplicate each other, with the 2nd one effectively idled by the first, or the second one filters what the first one wasn't set to do.
When
allowing special access, port forwarding etc., both firewalls need to be exactly in tune, or the access is disabled. When such an access issue is encountered, it pays to see if both firewalls are enabled, and to check if turning one off changes the dynamic.
The main reason to use both kinds of firewall in tandem is that you could then set different rules between computers
within a network that uses a common router/hardware firewall to protect the entire network's access to the Internet. But this is not standard procedure for a small, private network, while the hardware firewalls that
are used for this purpose often have more options and capabilities than a router for home use.
A reason a home user might have both firewalls enabled is when, for example, the router is harder (or impossible) to configure for a specific purpose than the OS firewall, allowing a special config to be handled by the OS (assuming it can do that). In the latter case, a good front end to the OS firewall would help, as software firewalls tend to be hard to configure.
In the end, however, even hardware firewalls rely on software, but their advantage comes from the dedicated hardware it runs on, and the fact that it's OS independent. Of course, if any of the software involved is flaky, all bets are off.