[Edit] To clarify the blackmail note: It's better to talk in the weekly 1:1 about salary expectations, changing markets or during people development focus, than to pull up a competing offer out of your hat while not talking about your dissatisfaction with pay during weekly 1:1s.
1. If the employee is only motivated by money, he will be gone rather sooner than later as there is always a higher offer around.
2. If you give in once to this, the employee will come back 6 months later with demanding the next pay rise.
3. You might have done something wrong in the past. An employee who can envision herself in the company in some years in a different role with personal development and fair pay rises (see 4.) does not leave.
4. You might also have no transparent pay rise process in place and clear guide lines why people have which salary. You might also have a wide band of salaries, which will bite you sooner or later.
5. Your salaries might also be too low and not working in the local market. This often happens when startups grow (or employee markets change) and salaries are not adjusted properly. Earlier employees - or employees before a VC round - often have too low salaries in this case. Fight for a budget rise to get every salary up in line again.
6. This might also happen if you agree to too low salaries when hiring. This often happens when you hire women, but also happens otherwise. You should always pay what the employee is worth, not what he is demanding (often too low). Don't feel happy if you hire below budget, this is a mistake. As a manager the easiest pay rise you can get for your team is during hiring.