why is stretching without doing a strengthening exercise immediately afterwords a problem?
well it's not, you could stretch after you lift, etc.. but if you spend alot of time stretching, improving rom, without "re-acclimating" those movements to produce force in those newly acquired ranges of movement, your power (explosive strength/reactive strength) production can suffer, max strength not so much, AND the new range of movement you acquired will be "more temporary, ie, less permanent". The idea here is to "reprogram the CNS", at a very fast rate, by stretching to improve range of motion but then following it up with moderate/heavy lifting, this reacclimates those movements for producing force with that newly acquired range of motion alot quicker, sort of how PNF stretching would leave you better at producing force after achieving greater resting length in the muscles, because PNF strengthens too, just like we're doing here.. that's why PNF, imo, is alot more beneficial than static regarding these issues, but static is still effective, i'm not saying it isn't.