Ti's strength and weakness is that desire to not be wrong. The strength is obvious. The weakness is that, in its subjectivity, Ti might actually be wrong about something, and all the paths it says "are not wrong" actually are wrong, and you don't realize it, because all of your logical requirements have been met. Fi has this same issue. It will insist upon upholding values that "feel right," but because it is subjective and may not have reflected upon the implications of those values well, it does not realize that the values (or combination thereof) are wrong.
For both Fi and Ti, this is where intuition becomes useful, introducing other possibilities that might be right, and in the event of a severe contradiction, will cause Fi or Ti to reevaluate and establish better internal values. To access intuition, one must drop the "right/wrong" thinking, and substitute the "WTF" or "maybe" thinking of intuition.