With the internet becoming what it is, and with apps available readily for pickup investing on the fly, and investing/economic news being readily available, it may seem silly to pay professional investors to manage investments for you. For example, Schwab and JP Morgan both have free brokerage accounts that link to your bank account that will execute trades for you for no fees.
The case for ETF buying is that, well, it's easy. If you find an ETF that meets your needs, it's pretty easy to buy a number of shares and then forget about it. Say you want to buy some stocks in renewable energy, but don't feel like doing the research on your own? Just buy some shares in a renewable energy ETF and call yourself diversified. They can also do some interesting trading things, like using options to grow the investments.
The case against buying ETFs is a big one. It's fees. All the ETFs that I have been learning about have fees, the best ones are less than 0.40 percent, but it still could end up being a lot of money every year. The more you have invested the more you pay in fees.
How can you avoid fees and still make great diversified investments? That's a good question. The best way that I can see is to see what the ETFs are holding, do research, and buy the individual stocks in the ETFs that you prefer.