Why is ageism a problem?
Any belief position based on stereotypes allows for missed opportunities for deeper, more beneficial relationships and contributions, and ageism is no exception.
Whether the assumption is that young people are more productive or that they are just self-centered and irresponsible, or that senior adults have passed their usefulness or are wise simply from being older, those stereotypes are limiting. If one makes the "younger is better" assumption, the benefits of both life and work experiences may be lost when older job candidates (or social connections) are ignored. On the other hand, age does not always guarantee wisdom; even when a more experienced person does have that trait, avoiding the contributions of younger people may cost in terms of enthusiasm and the ability to think "outside the box."
Realistically, a recent graduate and someone with 20 years of experience both have important skills, knowledge, and perspective to offer. The opportunity to collaborate, to get the best from both, is destroyed when ageism drives decisions.
Ageism is a problem for the same reason that any form of prejudice or discrimination is a problem. It entails making negative assumptions about an entire group of people that does not acknowledge the basic humanity of each member of that group. It also suggests that growing old is necessarily a bad thing, rather than a natural phase of life. More concretely, ageism can deny basic rights to people on account of their age. This is especially the case in the workplace, where certain jobs are not open to people over a certain age regardless of their individual attributes, which vary by person. The elderly are viewed as useless because they cannot carry out certain tasks. Not only is ageism degrading, then, but it also denies opportunities to people.