Interesting, but flawed, question.
Not all religious people do this. Even some who use science don't "need" science; they merely find it interesting. Some may need science, because they want to help others appreciate their religious views. Agnostics who appreciate science, but aren't sure about religion, may be swayed by science validating some aspect of a religious text.
Proving self right is a function of ego. And ego is not a religious thing. It's a human thing. Even scientists are swayed by ego. Just look at the "Clovis First" fiasco. Scientists who dug below the Clovis horizon were ridiculed and their careers threatened. This is science? Ridicule? Spoiled children is more like it.
But some of the religious are following ego rather than God. In fact, it may be that the majority fall into this category. They would rather stick with their beliefs than follow truth, because to change their minds would be to suffer the bruising of ego.
I'm a scientist and a Christian. I can't help but use logic, science and even mathematics in my biblical research. I'm not afraid to step beyond the crutch of continuity (science and logic) to the discontinuous realm of creation and miracles.
Science studies the products of creation (reality). Spirituality (the core of religion) studies the sources of creation. Science and religion are inherently complementary. Where things fall apart is with ego. People cling to old, invalid interpretations, like the Clovis First scientists and like the Young Earth Creationists (YEC).
The YEC would change their minds, if they weren't so trapped by their egos, because we now have a biblical timeline compatible with those of mainstream science. But this timeline shows that the Flood occurred 27,970 BC, right when a very specific species disappeared -- a species which matches the description given in Genesis 6. And yet, the coming of Adam is pegged at 10,434,130 BC. Science has a lot more digging to do. Scientists will find that religion proves them right. How? Because Truth doesn't belong to any one group and Truth is not affected by belief. God created Truth, and we only seek it.