Brovo and Jorick already did an amazing job arguing my point here.
But I'll give in my two cents anyways.

First I feel this need's to be divided into several topics in order to cover...

[b]Why Religion doesn't work[/b]

To start with, the very model of it is broken.

-Exhibit A) It makes a claim (God exists) and then seeks evidence to prove it. 
That is a flawed way to prove anything because all your study and research will have bias to it.

-Exhibit B) It relies on faith. 
Faith meaning willingness to believe in it [u]without proof or evidence.[/u] So it already outright claims it can't prove itself, therefore should be held to the mantle that science is.

-Exhibit C) Circular arguments. 
Mainly the "God is real because the Bible says so. The Bible is true because God says so" situation. You can't prove something with another thing that still needs proving itself. [u]Especially[/u] if the thing it is proved by it in fact needs to prove itself first.

If hypothetically we were to ignore that though, there's no way to make sense of Religion itself either. 
Note: For this example, we will take the Bible literally. For the "It's meant to be metaphors" argument, that will wait until later.

Now, if you want the long version of this just go to [url=https://www.youtube.com/user/DarkMatter2525]DarkMatter2525's Channel[/url] and watch any of his videos. Each one highlight's a contradiction in the Bible where the only thing you need to disprove the Bible is in fact the Bible. But for those of you not in the mood to go through one, several or many videos I'll make a summarizing list below.

-Exhibit A) Numerical Contradictions. 
Depending on the Bible you can even find issues of them getting the number's wrong of stuff like "How many horsemen raided X town". You could try to claim it's a typo... But if this was Gods words, would a typo even be there like that?

-Exhibit B) God is almighty/all powerful and all knowing, holy, just, innocent & loving. 
Now if God is all powerful, why does he allow so many evil and cruel things to happen? He either lacks the power to stop them, or does and allows them. So he already can't be both all powerful and all loving. Unless if you argue something such as he gives us free will. But look at cases like this more closely, Rape, Murder, Theft. Yes human's are granted the free will to sin and commit these acts, but isn't the free will of the victims taken away? They're ability to choose to live, keep their belongings or not have sex is taken away from them. All that happens here is free will is taken away from the victim rather than the attacker. So it would be more accurate to say "God loves murderer's, rapists and thieves more than their victims", which would contradict with being holy, innocent, just etc.

If you want another example. One humorous example that DarkMatter used was asking God "What's it like to snort cocaine off a hookers ass?". Well if he knew the answer to that question then he's not innocent, but if he doesn't know the answer to that question then he's not all knowing.

-Exhibit C) Sin's are changing.
There are quotes/passage's saying eating shellfish, having short hair etc. are sins. 
But then other area's where it's totally fine, or may be a sin to have long hair even.

For more extreme examples... Let's go back to Murder and Rape.
The Bible supports this, I've had people try to argue this on this site before... But when they're defense becomes like "Well... The Bible only supports Rape _____ times!" well... you've already lost. :P
Now anyone could bring up quote's where these are sin's, but there are also several times where God allows, if not outright tells his followers they are allowed to murder and rape. 

-Exhibit D) Cherry Picking
We see this all time. I mean with basically every last religious person on this planet we see it. If that wasn't the case, then the majority of the human populating would be getting killed for working on a certain day, wearing certain clothes, eating certain foods. Or doing stuff such as killing their child for disobeying, enslaving people, not letting women speak in Church or hold any kind of authority. 

-Exhibit E) Is it even your God?
Even if by some magical chance you've found a way to argue away all of these other points, basically every other Religion is in the same boat, hundreds of thousands if you include denominations. You still need a way to prove that specific Religion over any other... and this is even before we bring science into the mix.

[b]Why Science does work[/b]

-Exhibit A) We have proof and evidence.
What Science says is not based on what one person wrote in a book many years ago and did not let anyone question it. It is based on thousands of years of observation, studying, experimenting etc. If Science ever needs to prove itself it has mountains of evidence to back it up with.

-Exhibit B) Science is Humble.
While Religion claims to know everything, Science admits it does not. And rather than hide that it doesn't it is open with it and tries to find it out.

-Exhibit C) Science can admit they are wrong.
If proof ever shows Science to be wrong, they accept and absorb that new info to better advance society. They don't ignore it and cling to their original beliefs.

This is honestly a rather straight forward/short section... It proves it self, it changes to new info. There's no much else to say.

[b]Why Science and Religion do not mix[/b]

Exhibit A) 6000 Years VS Trillions of Years ago

Exhibit B) Flat Earth VS Round Earth

Exhibit C) Earth is the Center VS Sun is the center

Exhibit D) We all started off as we were VS Evolution

I'm sure you can add in many others.
The general point is basically:

TLDR: Religion on it's own disprove itself. Science on it's own proves itself. Put the two face to face, and they disagree on almost every turn.
And when such a disagreement happens, with one side having no proof or evidence (in fact it tells you to listen despite the fact they have none), while the other has almost all of human knowledge and evidenced to support it which one are you going to side with?