Yes belief in aliens is unscientific. There's nothing wrong with such a belief but no matter how you dress it up with Drake Equation calculations it's equivalent to a religious belief taken on faith.
That's not how it works. Most physicists didn't literally "believe" in the Higgs boson. Instead they expected it to be found based on the Standard Model theory of particle physics. That theory has been extensively validated over decades by thousands of physicists performing thousands of experiments. When a theory has been extensively validated then it has some predictive power.
On the other hand there is no theory about alien life, only a bunch of speculative hypotheses.