It is very normal for your son to fall asleep at the breast. In fact, just about all babies will do this if they are allowed to, as breastfeeding is very soothing and calming. Please rest assured that your son will eventually be ready, willing, and able to fall asleep on his own, but usually not at the age of six months. Your son gets a lot of comfort and reassurance from your presence, from being held, and from breastfeeding, so it is natural that these things help him relax and go to sleep. As he matures, he will gradually need this less and less. It may be helpful if you view your son's falling asleep on his own as something that he will gradually do with your encouragement and help, rather than something that he should do before he's ready.
There are some things that you can do to facilitate your son falling asleep on his own, such as having a regular bedtime routine. As he gets older, you may want to try breastfeeding until he is almost, but not quite, asleep. If he is sleepy enough to go on to sleep, you can put him down gently and pat his back until he falls completely asleep. There are also a number of helpful books you can read. We recommend Good Nights by Dr. Jay Gordon and Maria Goodavage, Nighttime Parenting by Dr. William Sears, and The No-Cry Sleep Solution by Elizabeth Pantley.
Once your baby reaches an age where he is able to be helped to sleep by means other than nursing, it would be helpful to any other caregivers to know how he likes to be comforted back to sleep. Be sure that the person caring for him is someone who will be understanding, accepting, and comfortable with what he needs.
We live in a society that puts a lot of value on independence. This may be fine for adults but is not as fine for babies. It often leads us to expect babies and small children to be more independent than they are biologically ready to be. It also puts a lot of pressure on parents to push their children toward independence even when they are small babies and toddlers. It may be that you are feeling some of that pressure right now with your own family. Joining a support group of like-minded parents can help reinforce what you read and learn about Attachment Parenting (AP), and the leader(s) and members can help you navigate through AP waters.