It's not a case of the UK wanting special treatment and to be separate, it's that we (speaking about Cameron's negotiations as the opinion of the country for readability) don't agree with many of the rules in place. It's not that we want one rule for us and another for everyone else, it's that we want new rules. Every country is in the EU because they believe it will benefit them. Countries have differing opinions on what should be rules. The UK is in a fortunate position to negotiate change and that's what we're doing.
To look at it from another point, why should everyone be subject to the same rules, when they clearly benefit one more than the other? The current state of Europe, the Greek debt etc., is massively in Germany's favour. The EU promised help to Greece, but ultimately failed to do so, and they were kept under the debt of Germany (I'm not saying it wasn't massively Greece's fault, merely playing devil's advocate here). Most of the EU's power resides in Germany, who have benefitted the most. Smaller nations tend to want to be a part of it for the financial injections or to enable them to operate on a global scale. The UK contributes more financially than it receives, and we are capabake of being a competing in a global market by ourselves.
For the record I think we should remain in the EU, but I think the anti-UK sentiment of us just being spoiled brats is nonsense.