Not being able to relicense under a license not acceptable to the authors of the particular copyleft license at issue is a main element of copyleft, but copyleft licenses often allow redistributing under more restrictive licenses that remain acceptable to the copyleft license author (e.g., the FSF encourages the use of "or any later version" language in GPL licenses, and GPLv3 is in many respects more restrictive than GPLv2; further, GPLv3 allows relicensing with specified kinds of additional terms that may in some ways be more restrictive.)
If you consider what developers are allowed to do with a piece of software, the main element of copyleft is actually not being able to relicense under a less restrictive license on the spectrum of FOSS licenses. The least restrictive "license" of all is no license, no copyright, i.e. public domain (in the US).
Because you can convert MIT/BSD to a closed source license, but you cannot convert GPL to a closed source license, in this sense the GPL is more restrictive than MIT/BSD. You can convert MIT/BSD to GPL (less to more) but not GPL to MIT/BSD (more to less).
I understand that closed source licenses are the most restrictive of all, this is just an alternative perspective on software freedom with regard to developers.
With an MIT or BSD licensed work, you can add more restrictive conditions, e.g. make a derived work proprietary, or add a "noncommercial use only" clause to your derived work, or whatever else you want. But with a GPL-licensed work, you cannot add additional conditions to the derived work, i.e. you must give all downstream reusers the same permissions you received. That's what's sometimes referred to as the "viral" property.
Unless, as here, you are the owner of the copyrights, in which case you can apply any license you want to the work.