They are not "denying" it--they don't have the power--but they are not consenting to or agreeing to it; i.e. they are not facilitating it. Only the court can allow you--or deny you the right--to do this. The opposing counsel are the attorney for the other person--their ethical and professional obligation is to do what is best for their client, not you, the opposing party. So if they feel that a delay will harm their client's interests, they are doing the correct thing. If you and your counsel (the one you fired) disagree, they can make a motion to be allowed to withdraw and try to convince a court that they should be allowed to do so.