This is really a tricky situation! The most important thing is to be honest, but also acknowledge their concerns. They mean well and are probably just thinking about saving money and keeping you "safe." Tell them exactly that - that you understand their worry, but this step is essential for your personal development. At 22 with your own job, it's completely normal and important to have your independence. That's not a sign that you don't love them!
Maybe make them a proposal: show them a realistic plan for your finances! How much do you earn, how much does the apartment cost, how much will you have left to save? That often puts parents' minds at ease because they can see you're not making this decision lightly. You could also offer to visit regularly or invite them over. Sometimes it also helps to explain to them that you'd be living closer to work or that having your own place helps you concentrate better.
The main thing: stay calm, be respectful, and don't put off the decision! The longer you hesitate, the more they'll pressure you. A short, loving, and firm statement is better than long discussions - something like "I love you, but I have to take this step." Period. They might feel hurt at first, but they'll get over it once they see that you can take care of yourself!