It's unfortunate that an opinion as ignorant as the one quoted in the title of this post is as popular as it is. I've encountered it in discussions with old friends from high school, after I hadn't seen them for so long.
Every now and then you will find someone who expresses confidence in the ability of the natural sciences to provide answers of meaning and significance. A related opinion is the one that more or less all there is to know can (and will) be known through the methods of the natural sciences.
One misfortune afflicting such an opinion is that it is hopelessly baseless, given its own criteria of justification. The natural sciences cannot give you the conclusion that they are the means to accomplishing all possible knowledge; no experiment will ever justify the conclusion that the natural sciences will eventually confer to us the answers to every question of meaning and significance. Rather, these are attitudes one antecedently adopts towards the sciences, which are not themselves justified or motivated by the actual results of the sciences themselves. But then the question is raised: why should anyone take such an attitude?
Someone may suggest: "Actually, this is an attitude motivated by an impressed admiration of the success of the natural sciences to come across actual pieces of knowledge about the physical world, success not shared by other so-called sources of knowledge such as philosophy and religion."
But suppose you have a metal detector that works excellently: its success in detecting what is metallic couldn't possibly justify the conclusion that therefore only what is metal is real. The fact that the natural sciences provide us with tried and tested methods of gaining knowledge about certain aspects of the physical world -- if it is a fact -- does not justify the conclusion that therefore there is no other knowledge to be had, even if this other knowledge is tricky, elusive, difficult to come by, whatever.
In other words, a person who takes herself "only to believe in science" is deceiving herself: science doesn't tell her to believe only in science; she evidently believes in something else, as well -- viz., this naive epistemological stance about the capabilities of the natural sciences.
Worse, too, is the fact that many things of value in a worldview have to go out the window if you limit your source of knowledge to the findings of the natural sciences. For they tell us nothing of value -- what is good, bad, right, wrong, moral, immoral, valuable, worthless. The natural sciences don't tell us it's good to help other people, for instance, though they may tell you that doing this causes certain chemical reactions in the philanthropist's brain, that it promotes tribal unity, or whatever. But none of that tells us whether helping others is good. To answer that question we have to engage in philosophy, or perhaps religion, and this takes beyond the bounds of the natural sciences, where different standards of knowledge and evidence are at play.