The process of only releasing information that describes groups of people is more broadly known as k-anonymity [1]. This comment does a pretty good job of describing its appeal (it makes some intuitive sense, and it's better than doing nothing) and drawbacks (it's vulnerable to side information, releasing even two k-anonymous outputs can reveal a lot of information, and it can get pretty complicated).
Differential privacy solves these problems because it gives mathematical bounds for the amount of privacy lost. If you take part in two 0.5-differentially private computations, the probability of any event becomes at most e times more or less probable as a result of those computations. Of course, differential privacy has a lot of work left to do before it's feasible to just insert it into general data analysis, but it's slowly moving along that road.
Differential privacy solves these problems because it gives mathematical bounds for the amount of privacy lost. If you take part in two 0.5-differentially private computations, the probability of any event becomes at most e times more or less probable as a result of those computations. Of course, differential privacy has a lot of work left to do before it's feasible to just insert it into general data analysis, but it's slowly moving along that road.
[1] https://en.wikipedia.org/wiki/K-anonymity