SIW, this is the first time I've read about someone else's LO doing this - but my dd2, now 7 months old, has been exactly the same. She has silent reflux, which I had a horrible time getting help for until she was diagnosed with a floppy larynx (which will put itself right by 18 months at the latest, almost certainly) whilst in hospital with suspected RSV.
I could tell you a whole long story about the GPs fobbing me off, in spite of her breathing being made a lot worse by the inflammation the reflux caused - but thats not the point of your OP.
Basically, I discovered she could only drink comfortably lying down almost or entirely flat, when she was about 6 weeks old and the reflux started to get really bad - otherwise, she would arch, twist, yelp, etc.
Now, at 7 months and on Ranitidine and Domperidone for the reflux, she can drink in my arms or even sitting up in her high chair - but she still prefers to lie down, head to one side. She first managed feeds in my (or dh's) arms at dreamfeed time, ie really relaxed.
I have no idea why that is - maybe its the shape of her larynx that makes feeding lying down easier, in dd's case - but can say without any doubt at all that you're not alone. Maybe its the stress of reflux pain that makes them want space, not to be held whilst feeding?? I've no idea, jsut guessing. Whtever the casue, hopefully it will get easier as your LO gets older, meantime I found I could feed dd in the buggy (almost flat) or, in a restaurant, lie her on a bench type seat, etc.