There are parts of davenning which are simply untrue; maybe they once were, but they are no longer. Maybe they are rue for others, but they aren't for me.
Sometimes we can relate to them as prayers - not something we are, but something we aspire to be. But sometimes that simply doesn't work, either.
1) In tachanun, Nusach Adshkenaz says, from Tehillim, "With my tears I will soak my bed". I don't cry over my sins, and it seems ludicrous to beg forgiveness for those sins based on my
crying over them.
2) On Tisha B'av, we say a version of Nacheim which describes Jerusalem as being 'desolate from lack of inhabitants'. That's not Jerusalem's problem anymore. Most of the lament is relevant, but that part isn't.
3) At the end of bentching we say 'I was young, and I aged, and I never saw a righteous man abandoned or his children begging for food'. What if I have seen an abandoned tzaddik, or his children going hungry? Doesn't it happen?
So what's the conclusion? Skip? Change? Ignore?
As usual, the best solution seems to be the most common one - simply daven without kavvanah.
Leave it to the Jewish people, eh? Heirs of the prophets!