He says that you don't understand. I would bet that he doesn't understand either. I agree that at this point in your lives, dating other people is a good idea. However, saying it and doing it are two different things.
If you are still seeing and/or talking to each other every day, you are an "item". The known is so much more comfortable than the unknown.
It Isn't Easy to Break Ties
The two of you need to make a clean break from each other-no phone calls, no contact. Only then will you truly be able to give other people a chance.
This will be painful and this will be hard. You have become a part of each other's lives. Given your ages, you have probably gone through some pretty significant stuff together. That is a hard relationship to lose. However, the option is to continue forever in this non-relationship, potentially leading to a marriage just because he's there.
What if He's The One?
If this is really THE ONE, your paths will cross again. Marriage requires the right person AND the right time. Don't fool yourself into thinking that if you hold on to him someday the right time will come and then you'll be ready it doesn't work that way.
Give Yourself Time, Lots of Time
Did you ever hear the old adage, "If you love something set it free..." By continuing your relationship you have set each other free in words only. It is time to do it for real.
If you are unable to trust that God will bring you the right man at the right time, set a date to call each other again. However, this date must be no sooner that 6 months to a year from when you break contact. This is the minimum amount of time that the two of you will need to mourn this relationship, do the personal work needed and begin a new relationship. Any sooner and you run the risk of rushing back into each other's arms for comfort.