I don't agree that people despise the rich purely for being rich, I certainly don't and don't know anyone who does.
What I believe people dislike is the behaviour of the rich, ostentatious parading of wealth is seen as a slap in the face to those struggling. The behaviour of the top bankers earning mega money prior to the crash was ugly to say the least and they don't seem to have adopted any humility since.
If you want to be served in a restaurant, or want someone to clean your house for you, then value them and what they do. The arrogance of some very rich people is stomach churning.
The lack of social mobility is a real problem, people feel they have no opportunity to move upwards and that breeds resentment. I lived in an extremely wealthy Country, everyone was supremely motivated to 'better themselves' for the benefit of themselves and their families, people aspired to be wealthier. Interestingly, the tax rate in that Country was a flat rate of 30%, irrespective of income, everybody paid it, the penalties for attemting to avoid it were draconian, but there was no 'flashing' your wealth, and no job was looked down on.
My pet hate is the vacous celebrities, footballers, etc., particularly when they berate and guilt trip the rest of the public into supporting their latest charitable cause.