Joining the conversation late, as usual, apologies
Woodsy writes:
In this and other forums, when athiesm is discussed, theists often use the phrase "choose to believe" or "choose not to believe", usually with reference to their god.
I find these phrases puzzling. I would suppose that one believes a proposition (or not) when one encounters satisfactory evidence for its truth (or falsity). How can one choose to believe something, or to disbelieve it? Can one choose to believe something one knows is false?
Let's start at the beginning of your argument. You said that you find phrases like "choose to believe" puzzling because to you, belief is always based on coming in contact with satisfactory evidence.
Here is how merriam-webster defines "belief:"
Merriam-Webster writes:
: a feeling of being sure that someone or something exists or that something is true
: a feeling that something is good, right, or valuable
: a feeling of trust in the worth or ability of someone
and
:a state or habit of mind in which trust or confidence is placed in some person or thing
:something believed; especially : a tenet or body of tenets held by a group
:conviction of the truth of some statement or the reality of some being or phenomenon especially when based on examination of evidence
So here we see that belief in response to evidence is only one of the many definitions given for belief. That may actually answer your question right there: Theists use the phrase "choose to believe" because, by definition, that is what belief is. You are choosing to put trust in something. This may or may not be upon examining evidence.
It is curious, however, the merriam webster's first three definitions include the word "feeling," suggesting that belief is rooted in personal conviction rather than a decision made using critical thinking. In my experience, it has included both

Regards!
- Raph
Edited by Raphael, : No reason given.