Life as a problem may be too broad a statement to be meaningful (in some context - though this hardly seems to be that context if there is one). Nevertheless, it is how buddhism views life at a fundamental level. I can understand why buddhism conceptualizes life this way even if I don't agree with it.
The pessimism in the viewpoint is inherent, whether it's warranted or not - and it helps to remember that a view can be pessimistic even if it's true. We might prefer to use other terms because of a negative connotation - but a view which states that life is a problem to be diagnosed is necessarily more pessimistic than one which asserts that life is the solution to some problem, for example. Perhaps the first view is factually accurate, and the second a wishful fantasy - but still. OFC, as you note..it's rare to find any pov that leans entirely to one side or the other in that divide. There's certainly some optimism in the notion that the problem of life can be fixed, but this view only makes sense in light of the earlier proposition. One wonders whether any tradition which does not offer some similar tangible or intangible solution would be able to compete with those that do.
We could repeat this with other beliefs, all without ever referring to or debating their factual accuracy, their internal consistency, or asserting that either state of affairs is or should be negatively weighted. The notion of sin is inherently pessimistic, but the hope for salvation is decidedly not.
Miasma, again, inherently pessimistic - and the solution to the problem of miasma if generally tragic (in the classical sense of the term, no less)...but again there is at least the hope of breaking free.
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