I think one reason for the resistance of many cyclists to "segregation" is the fear that they may eventually be forced to use a load of inadequate and possibly damgerous cycling "facilities" and forbidden from using the road because these inadequate segregated infrastuctures exist. The fear of stupid legal compulsion is not irrational as it was already attempted at the last revision of the highway code and the CTC had to fight hard to get the proposals changed.
The assumption that cycle facilities here will always be inadequate is also a rational one based on experience. The majority of my 12.5 mile commute has cycle lanes along it but, apart from the short sections of bus lane, not a single metre conforms to the DfT's own cycle lane design guidelines. There are whole sections that are positively dangerous, some of which I have documented in my blog. Proposed schemes do stupid things like expecting cyclists to give way to the traffic that approaches along every single side road, which makes cycling as a mode of transport completely impactical.
It is quite likely (though I do not have scientific evidence) that a big part of the problem is that most people who think about it at all believe cycling, and particularly expansion of cycling, is about families with 2.4 children going out on a Sunday afternoon for a leisurely ride, and can hardly even conceive of the idea of using a bicycle to get from one olace to another. It would seem that planners particularly share this view, which is based on their assumptions and prejudices rather than evidence..