There are cases where that is true and certainly it's a personal decision about how public or private to be about one's philanthropy. More often than not, someone being more public or visible about their philanthropy is done for a reason, i.e., to show leadership and commitment to a particular cause. And to do so as a means to an end, to help raise more philanthropic capital. This is true especially for newer organizations and causes.
Like most things in this world in we each invest, we want to know who we are investing in (not just what). And knowing who the other "investors" are is an important signal that may guide our own decisions. Visible philanthropy might occasionally be motivated by arrogance, but more often it's a signal of public leadership and commitment.
P.S. A lot of those people that are the most visible in their philanthropy in one realm are also very private or anonymous in other areas of their giving.
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