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The Borg were not a match for Species 8472 in Star Trek: Voyager’s episode "Scorpion." They needed humans' help to design a weapon against Species 8472.
If humans were smart enough to design a weapon against Species 8472, why can't they design weapons to resist the Borg, given that Species 8472 were victorious over the Borg? This is illogical.
I think the premise is flawed. Species 8472 turned out to be vulnerable to a blend of Borg technology (beyond our capacity to design, but not beyond our capacity to re-task) and highly experimental Human technology (The EMH). Species 8472 may well have the ability to destroy Borg cubes, but at no point do humans gain the sort of unfettered access to their tech that they do with the Borg's.
That all being said, humanity has shown both a desire to design weapons to help them in their fight with the Borg and a strong capacity to do so.
Humanity (i.e. the Federation) has been able to resist the Borg (as Valorum's answer shows with a few examples which I shall not repeat).
Comparing the Borg to Species 8472 is like comparing apples to gneiss. Their vulnerabilities and strengths are not variations of degree in the same mode.
The Borg have been shown to lack ingenuity or inventiveness. It seems that this is one of their essential flaws: once assimilated, the knowledge, technology, and biophysical capabilities of the subject are copied and utilized, but the more mental traits seem to be ignored and idle.
Their ability to adapt in the past has been limited to an adjustment of permutations — e.g. changing shield frequency to match and neutralize (through destructive harmony) the incoming phaser frequency.
That is probably why the Collective finally agreed to Janeway's accord, and why it assigned an adjutant (7 of 9) to work with the Humanity: the Collective was learning that it could gain more from them if they went unassimilated.
The problem you think exists is none in reality, but instead two different situations there, that SEEM similar but are not.
The Borg are able to adapt quite fast to all weaponry. This means a specific weapon may work once, or twice but then the Borg have adapted. Thus humanity HAS already designed weapons against the Borg, but they have proven not efficient enough quite fast (as they try to out adapt beings used to adaption).
Species 8472 on the other hand has had technology that by itself was beyond the Borgs. Thus they were declared a primary target for assimilation. BUT the problem is their technology was so high that they could simply destroy Borg cubes sent to assimilate them; which they did and counterattacked.
As Valorum has mentioned in his answer: Borg lack ingenuity. Which is what humans have in abundance. Thus with our own way lower than Borg technology level, we can sometimes even the playing field against the Borg a bit until they adapt. With Species 8472 on the other hand...they had a technological advantage the Borg were unable to counter as no other species they had assimilated or could assimilate had appropriate technology. So they needed ingenuity which they got in the form of the Federation crew joining sides with them.
What is more though is that the Federation was too low in tech level to make a difference, thus the Borg changed that by helping out with their own tech. Thus the Borg Tech and human ingenuity make the difference there.
But back to the question: The problem is that the 2 situations are completely unrelated. Borg are adapters without ingenuity, while Species 8472 have a VERY high technology level, but are not as adaptive as the Borg or humanity. So aside from the Federation being the underdog with quite some improvisational talent in both situations. Those two situations are radically different from each other.
