First of all, there is no call for it to be changed. There is no noise about people paying income tax on investment income. The noise is coming from exit tax and deemed disposal on ETFs. Given the revenue just did a review of this, I don't think that will change.
It favours the better off. Elon Musk famously claims that he doesn't draw a salary from Tesla. That's because he doesn't need to. If you are a professional landlord or have many sources of passive income so you don't have to work, you will also be paying less tax on your investments than people who have to go to work in the morning. This would clearly be a big tax break on the wealthy. It will obviously mean less income for the Exchequer, which means reduced services, for those who need it, which isn't the wealthy who got the tax break!
Taxation on income in this country is far too high. You shouldn't have to pay over half your income to the government. But any changes in taxation, should be something that all can benefit from (with our low standard rate band, lowering the higher rate isn't exclusive to the wealthy) and not just those with the assets to avail of these breaks.