Go back and ask for specific examples of how you're too fixed in your views. It's a bit vague and meaningless otherwise, and they can't expect you to improve if they can't tell you what they mean. They need to give specific examples, and just saying, "Well, I don't hear anything good about her work," (just quoting feedback I got last week following some of the best feedback of my career...) means there's nothing you can work with. I'm quite sure I don't do everything perfectly, and I can provide lists of stuff I need to improve on - but they're specific examples around communication and technical areas, so I can work on them. "Nothing good" could refer to technical, or communication, or time-management, or... there's no focus. (And it probably just means the people I've had good feedback from haven't spoken to him at all.)
At ours, we have a list of technical competencies and one of leadership competencies, and a guide to what sort of thing you should be able to achieve at your grade - so for a particular grade, you might need to be advanced in at least 3 competencies, competent in 5, and learning in no more than 2. It gives you a good idea of what you might need to achieve to be considered for a grade promotion, and where the gaps are, that should be feeding your development plan. I've been through each of ours and rated myself against each of them, with examples as evidence.
Also, take advantage of any training available, be it classroom, online, book-based or whatever. Look for something on managing change, to show how you're addressing the criticism of fixed views. Maybe also communication skills or negotiating skills, or assertiveness or dealing with difficult people?
Are there any other opportunities outside your core job to show your skills? We have various voluntary community projects going on, working with schools and so on, encouraging them to consider IT careers, and also boosting our image in the local community. I've been involved in organising a couple of events, and it really does give the chance to be in control and prove what you can do, which if you've got a narrow-minded manager who won't give you the chance to express yourself can be really valuable. Also, it gives you the chance to network beyond your own department, and get allies elsewhere, who can advise you on other ways of approaching it.
But you do also need to consider looking elsewhere - either within the company for another department, or further afield. I found it very instructional being offered a job I wasn't actually that keen on, which made me much harder-faced about salary negotiations. I was really taken aback when they took my very high salary request seriously, and it made me look at myself differently. Also, just updating your CV makes you focus on your strengths and achievements, and it's good for that reason alone.
I am going through something very similar at the moment, and if I'm not happy with the response I'm due to get next week, I am strongly considering putting in a grievance (it was HR who suggested that to me, so I think they think I've got a case, which surprised me.) I can totally accept that there maybe a quota on the number of higher grades they can have in a department, or they just don't have the budget, and if they come back with that, fine - but it's absolutely not acceptable not even to give me a fair hearing when I've put all the evidence together. If there are areas that mean I'm not ready for it, that should feed my dev plan; if it's just because of budget/organisational quotas or whatever else, then so be it, but they can at least acknowledge that I am otherwise good enough, and that's the only thing in my way. But you do need to be sure if you're going to go down the formal grievance route, because if things are bad now, they're likely to get quite a bit worse if you go that way, and they will do all they can to discredit you.
One other question HR asked me when I saw them earlier this week was do I think it's because I'm a woman? Do you think there could be any discrimination like that in play? It's definitely not unknown in IT departments, unfortunately.