I am taking it for granted that your male friend is an adult, capable of making independent decisions. If he is not ready to introduce you to his family, if he is afraid that they will judge you, there may be something about you that makes him feel uncomfortable about his relationship with you. You may be stuck in the friendship zone, and have to settle with that, since you consider the relationship "very loving."
But if you want the relationship to progress to your involvement with his family, ask him to give you the details of what it would take to make that happen. If he insists that it cannot happen, then you have the prerogative to end the relationship and move on, or continue being stuck in his secret pocket. I hope that you are wise and brave enough to make the right decision. Talk with someone with whom you can share all the facts, and who can offer you guidance.