That's false. Derivative software that doesn't use the BSD licence has no bearing on the BSD-licenced software itself. For example, Sony using FreeBSD for the PS3 operating system has zero impact on the freedom of a FreeBSD user. The GPL, on the other hand, directly infringes on the user's freedom to fork and redistribute the software.
That's also false. The GPL doesn't only restrict non-free licences, it restricts any licence change on the derivative work. If I fork a GPL project and want to redistribute my changes with a free licence such as MIT, the GPL will prevent it to protect itself. It's an authoritarian licence that doesn't respect your freedom.
I fail to see how the share-alike nature of the GPL is "authoritarian" and "doesn't respect your freedom".
It is built to guarantee the freedom of the user. It's imperfect, as it has to work within the constraints of the copyright system, but it's a hell of a lot better than licenses like MIT for propagating freedom to end users.
Here's a real world example:
If I want to root my android device with KernelSU or build a custom ROM, I need to recompile the heavily customised kernel built by the vendor for my specific device. Because Linux (the kernel of android) is under the GPL, the manufacturer is compelled to give the user the same freedoms that were given to them, which means I can download the source code and do this.
If Android were based on, say, the FreeBSD kernel instead, this would be impossible. There would be very few, if any, android custom ROMs, because the vendor could, and would, withhold the modifications they made to the kernel.
You're again assuming that the GPL only restricts non-free licences. This is not the case. If I add a feature to a piece of GPL software, I can't use BSD on my new code even though the new code isn't derivative work. Hell, if I write a completely independent piece of software that links to GPL software, my new software has to be GPL even though not a single line of GPL code was used. All of this also applies to free licences like BSD. The GPL doesn't protect freedom, it protects itself.
You're assuming that the GPL protecting freedom and protecting itself are mutually exclusive. They aren't. Again, the GPL is written to ensure the code remains free forever.
Also, I've already pointed out the flawed nature of licenses like MIT and BSD, and if the GPL could be relicensed to them, it would provide a very easy way for proprietary developers to strip the freedom from the GPLed code when passing a derivative on to their users.
It is unfortunate that it cannot be relicensed to other copyleft licenses, as that would not pose such a problem, but without an explicit list of licenses it can be relicensed to I'm not sure that's even legally possible under copyright.
It is mutually exclusive. You cannot "protect freedom" and impose restrictions on freedom. Also, no, you just explained how the licences worked and didn't provide a single argument as to why having the freedom to licence your work however you want is a bad thing. The GPL doesn't ensure that the software stays free, it ensures that it keeps control of the software and all future additions to it even if they're completely unrelated.
Redistribution only becomes an issue if you try changing the license or selling it. GPL primarily protects against businesses profiting off of it. There are use cases for both licenses.
Copyleft protects the freedom of the user, regardless of who is the developer, I think that is way more important if what we want is to make software for humanity rather than pragmatic business choices.
It is a point of what you regard as real freedom, do you wish to eventually lock in your users or let who might fork/take over your project do that?