Your cycling fallacy is…
“We shouldn’t provide for cycling, as it disadvantages people with physical disabilities”
Evidence from the Netherlands (and increasingly from the UK, where new infrastructure has been built) shows that high quality cycling infrastructure is often shared with wheelchairs, mobility scooters and other assistive modes of transport. Cycling infrastructure works for all these types of mobility aids.
And in general, cycling infrastructure should go hand-in-hand with other improvements to the physical environment too – like smooth, continuous footways across side roads, for example.
There are cycles available for almost every type of disability – it’s actually an inclusive mode of transport that will often act as a mobility aid for people who find walking difficult, people who can’t walk far and even those who cannot walk at all.
So in fact the truth is the opposite of the myth – cycling actually gives people with physical disabilities more transport options and independence, not less.