If it wasn't already obvious before, it's made crystal clear in " Still" that these two would die for one another. When Castle returns with coffee to share whatever fate is in store for Beckett, he proves he has no intention of living without her either. At this point we can pretty handily rule out puppy love. Now this is what you call commitment.
2. Castle is a light in her life.
Beckett's life has been full of a lot of dark things--her mother's murder, killers with elaborate plots of violence, and a tough, male-dominated working world to prove herself in day after day. When Castle is around though, things lighten up. Beckett laughs. She sees magic even if she still doesn't believe in it. She finally realizes what's most important in her life--and it's not justice. When Castle is around, Beckett gets to be "Kate."
3. The 12th Precinct is already her family and so are Martha and Alexis.
A seriously wonderful family has formed around Beckett--Castle, Lanie, Ryan, Esposito, Martha, Alexis--there is no sense walking away from any member of that family. She's happy. Don't mess up a great present because some stranger came along asking about what the future would look like. Wouldn't the best future still have all these people in it?
4. They have a great thing going professionally.
Love and family aside, Castle and Beckett are a great team. Their working styles complement each other, making them each better in their separate roles. On a personal level, this is beneficial for each. On a grand scheme of things level, New York and ultimately the world is benefiting from this. The work they do may not be federal, but that doesn't mean it isn't extremely important.
5. Job opportunities will come and go, but there is no one else in the world like Castle.
If someone as loving and playful, boyish and ruggedly handsome, curious and innocent, devilish and charming as Castle walks into your life (or is brought in by handcuffs...), you don't just let that go. Put the handcuffs BACK ON (or rings, rather) and keep him forever!!
(Psst! There is also a list of 5 Reasons Beckett Should Take the Job.)