I am not a pediatrician, just a mom. Consider an alternative perspective. Babies in many parts of the world are still nursing at 2 years. Now in the US, that is considered WAY out of the mainstream I know.
I completely respect your pediatrician's recommendation, but I urge you to consider that your baby does not understand timetables or pediatrician's bell curves, and you can bet that most of what a pediatrician recommends is based on bell curves. Where is your son on that bell curve? I encourage you to put more trust in yourself and your listening abilities with your baby. You know your son, you see how he responds to food or formula because you are with him every day. Your pediatrician, although highly trained and knowledgeable with regard to kids in general, can only speculate on developmental milestones when it comes to your son in particular. *Every* child is different.
I encourage you to listen to your baby and try to figure out what he's telling you. Is he interested in the sippy cup? Is he able to pull the liquid sufficiently without choking or discomfort? Is he interested in food, showing signs of frustration when you are eating (maybe he wants some too?) And even if he does, that doesn't necessarily mean he wants what you are having - he just wants to share in the experience to the degree he can. I advocate that it's up to you to help him do that comfortably and in a way that he can enjoy.
If he doesn't like the formula and you are concerned for his nutrition, what about trying another kind or brand? There are several organic varieties, dairy and soy, and at least 6 non-organic varieties - and those are just the powdered ones I know about. And each one tastes different. Maybe a change in flavor will get him more engaged.
Our first child was anxious to start eating and at six months was taking 3 meals a day of pureed solids and moved on to finger foods by 8 months. However, she didn't use sippy cups until much later because they made her choke. She just couldn't figure out how to suck with her mouth and close her windpipe at the same time. She did eventually, although now she's moved on to a regular "non-sippy" cup for mealtimes. By the way, at 26 months, we still allow her an 8 ounce bottle of organic toddler formula 3x a day - we figure it's a super way to get lots of liquid into a very active body in this, a very very dry climate. Some days she wants it, some days she doesn't. We figure there is plenty of time for her to give it up herself before she has to be in kindergarten. There are lots of people out there who would be appalled by this approach, I'm sure. It seems to me our culture really appears to want to rush our babies into growing up FAST. I don't want to keep my baby a baby, but I also think that rushing them out of binkies and bottles and bankies before they are even 2 years old is unnecessary. I figure, what's the rush? I'm not trying to impress anyone with my daughter's developmental milestones, and I don't care if someone thinks she should or shouldn't have a bottle by what age. I'm her Mom, and I (with her Dad) get to decide. You are your son's Mom, and you get to decide what works for you and him.
I personally find it very difficult to believe that drinking from a bottle after the age of one could create any sort of lasting trauma or damage. Maybe it's about the baby teeth? My response to that is, how long does it take a hungry active child to suck down a bottle? We're talking a matter of minutes here, maybe 15 tops if you have a super slow eater. How can 15 minutes of occasional sucking on a bottle (remember, a baby that age is typically eating some solids so it's likely not his only nutrition) create enough pressure to damage tooth development? I can certainly understand concerns if parents give a baby a bottle and let them keep it for long periods as a form of pacifier.
By the way, our older daughter gave her binky up all by herself at 20 months - we had been talking about it with her and one day she put it in the trash and we rode with that move - every time she asked for it we said, "you put it in the trash remember?". No fits, no tantrums, and after a week, she didn't even ask for it at all. As you can see, we are big fans of letting them think it's THEIR idea, and then jumping on the bandwagon. Kids all have their own timetable. I"m not suggesting we parents let our kids run the show, but what works for us is picking our battles carefully and trying to make as much of it seem like their idea as possible. That way when it does come time for a parent to have to lay down the law, it's a special time for the child to learn to listen - I believe that increases the odds of the lesson being learned.
I'm sure this approach will backfire sometimes (who knows, we may be struggling with a bottle 3 years from now!), but what approach doesn't? That's when you move to Plan B. As a parent, you already know the value of Plan B. And C, and D..
Also, as it relates to your son, our second child only really became interested in 'solid' food AT 7 months (we tried months sooner, but she would gag and fuss so we didn't push it), and even now at almost 9 months, anything that is not completely pureed causes her to gag and choke. We do lots of variety but all pureed (there's a book called TOp 100 Baby Purees), and she's happy as a clam. Mealtimes are a fabulous and fun mess. She loves it! We plan to keep her on the "Pureed Plan" until it is clear that she can comfortably enjoy other foods and/or she expresses a desire for something different.
Sorry, I was all over the map here, but the main thrust of my message is that if I were in your shoes, I'd try listen to my baby and try to understand what he's trying to communicate to me, and respond to that. A 9 month old is not trying to play games or manipulate or 'be difficult'. They are just being. They smile when they are happy and they cry when they are sad or frustrated or in pain. During the process, as a Mom, one gains more trust in onself and gets better in tune with the child so that if there ever really is an issue to be worried about, Mom is right in tune with it because she's in listening mode.
A little about me: I am a full time working mom with a super SAH husband/Dad and 2 marvelous girls. 26 and 8 months. My 26 month old was breast fed until she was about 10 months, at which point she started to wean herself, desiring a bottle and her solids over nursing. My 8 month old is still nursing about 60% of the time, the rest is organic formula and solids.