Think of a similar word "faithful". Being faithful means you can be relied upon. When one is described as being faithful, there is normally some form of evidence behind it, whether tangible or not. And thus "faith" is the evidence of things unseen. You therefore can have "faith" in someone that is "faithful" because you know it to be true. You saw it, you felt it, you know it, ect.
Actually that's not the definition of science, it's a definition of science, and whether it is a complete definition of science depends heavily on one's thoughts on philosophy of science. Falsification as the central concept has at times been popular and at times unpopular; right now, it is less popular than it was, say, about eighty years ago.
Luckily it doesn't work like that at all. Science progresses when incorrect theories are falsified. No army of philosophers will ever be able to change that with a silly meta argument.
Besides, not all scientific progress is made by falsifying incorrect theories. Quoting Max Planck:
> A new scientific truth does not triumph by convincing its opponents and making them see the light, but rather because its opponents eventually die, and a new generation grows up that is familiar with it.
(Of course, whether to call this a "scientific progress" is a matter of debate, but frankly if it advances mankind's state of understanding nature then that's good enough for me.)
Falsificationism is one possible solution that's been proposed, but it is not the only one, is not universally accepted, and you really should probably do some background research on the topic before arrogantly spouting off about how you have the one true answer that some "army of philosophers" with "silly meta arguments" can't manage to come up with.
Belief, in general, is a psychological attitude towards a claim.
Your definition of faith is more like my definition of fundamentalism: All evidence to the contrary of X is meaningless because X is true.
The distinction is subtle but note that faith uses the concept of faith as adjunct to rationality, rather than as replacement.
Faith: X is true! Because! Science: Is X true? Are we certain? Lets try and find evidence counter to X.
I see a lot of people (from each side) trying to prove their point, rather than disprove it.* The former is faith, the latter is science.
* Not referring to people here, just the population in general