I don't know much at all about teacher's salaries to comment. I do think, however that there is a perception by some that private sector salaries are always better. Definitely not the case, not any more.
Also, it depends what bit of the private sector you are comparing to. There's the City, with health insurance, gym membership and all that palaver, and at the other end there are millions of private sector employees who have low salaries, no contributory pension, statutory sick pay only, statutory maternity pay only, statutory holiday entitlement only. Plus a whole range of people with something in between.
With teachers, who do they feel they should be compared to? It's a genuine question. If it's, say, lawyers, should it be city law firms or weeny struggling high street ones? Pay and benefits in the private sector vary so much by area, size of the business, how successful or not the business is, so many factors which don't come into it in the public sector as a rule.
A detailed comparison would be interesting, but I think such a comparison should take into account total package. Even leaving aside the arguments about how much of the 13 weeks not in school is actually holiday, it's impossible to argue that teacher's benefits aren't fantastic. People in the private sector can only dream of final salary pension schemes, and the teachers' one is incredibly good, plus take into account all the other benefits you get in the public sector. Not as glamorous as a gym membership or company car, but often worth much more financially and also more important personally to the individual.
And in answer to the OP, no we don't have the right to pay increases. Another point to make is that I've never worked anywhere that had an automatic cost of living increase. Pay rises where I've been have been dependent on performance - you perform well, you get a raise, either a weeny one, or a bit more if you are outstanding. If you don't perform you don't get a raise. No increases just for sitting there for a year.
I want to avoid sounding bitter - there is absolutely no way I would work in the public sector and I admire anyone who does, it definitely wouldn't suit me and I don't begrudge anyone their lovely benefits. But I think there is a tendency not to look at the whole picture sometimes.