Note, when I say "feeling pride" I don't mean simply being happy for someone, or admiring them. Feeling pride must have some element of identification: you're proud because in some way you associate yourself with the person. Their glory is both reflective and baskable.
In some cases, one may indeed have contributed to another person's achievement. The parent who encouraged their child, and took them to football practice every Sunday, may rightly feel that they played their part in that child's eventually winning Sports Personality of the Year, and take pride in that. But much of the time that simply doesn't apply. While I can take some credit for my own achievements, and perhaps those of my children, I certainly can't take any for those of my remote ancestors, or the fighter pilots of WWII, or Jessica Ennis - but I still find myself taking pride in them, almost against my will. In fact, I find myself thinking of this sketch, and feeling a bit silly.
At a biological level, there's no great mystery about it, I suppose. This kind of bonding exercise must have had an evolutionary advantage for social primates such as ourselves, and continues to do so. It can be a hugely pleasurable experience, and an enticing one too, offering a serotonin hit in exchange for nothing more onerous than a willingness to identify with the group. But I still feel uncomfortable at the awkward fit between "taking pride" in this sense, and the way we like to think we think about issues of autonomy and responsibility.
What's that? Greg Rutherford won the long jump? Woot!