In my experience “I believe X” suggests that the speaker has chosen to affiliate with X, feeling loyal to it and making it part of his or her identity. The speaker is unlikely to offer much evidence for X, or to respond to criticism of X, and such criticism will likely be seen as a personal attack.
In his post Robin argued that people often convince themselves that they truly reconsider their strongly held beliefs, but what they do is false reconsideration with the real purpose of reassuring themselves and strengthening the belief. Before it was just a strong belief, but after false reconsideration it’s a strong belief that they’ve really, definitely, seriously reconsidered. But if you can’t imagine yourself going through the day holding another set of competing beliefs than you never actually reconsidered it.
As mentioned in one of the reads, it may be better to say ‘I feel’ than ‘I believe’. They mention this because it makes clear the personal attachment. I would add that feel instead of believe takes away the broad brush-ness of, say, religious statements that in reality are subjective (then by default not objective) and are highly unlikely to have been shared with their religious forefathers thousands of years ago. Here is a decent thought to close on:
Conservatives, could you imagine becoming someone believes that higher taxes and unemployment insurance don’t hurt economic growth or employment? Liberals can you imagine becoming someone who believes that that minimum wages decrease employment and fiscal stimulus doesn’t work? If the answer is no, you should think about whether it’s because holding such a belief would conflict with your identity or affiliations.