One of the more frequent mistakes made is the assumption that because a thing is not negative, therefore it is positive. This is frequently done in philosophy or theology--and nearly as frequently incorrect--and the result is that even when the premises are right, the conclusion is wrong. Ironically, the philosophy comes from a worldview which looks at the truth as if it is a number line: there are some things which are right, and their opposites must be wrong--just as some numbers are positive and others are negative.
So far, so good, but it does not follow that a thing which is the opposite of a wrong statement is a right one. Indeed, even with numbers this does not hold. Not all non-negative numbers are positive, for zero is neither a negative number nor a positive one. Similarly, remaining silent means giving neither the right answer nor the wrong one. Nor is it correct to say that a telling of the truth which omits some of the facts is the telling of a lie--though if intentional, it is certainly not honest.
There are countless examples of this, but I will limit myself to a few teachings of the Church. Her claim to infallibility means that she will never teach something which is untrue as a matter of faith or morals, to be definitively accepted and assented to by all Catholics; this does not, however, mean that she will always be able to teach to answer every question pertaining to Faith and morals with the fullness of all truth, but rather only of revealed truth. Thus, the teaching of infallibility is a guarantee against lies, not a guarantee of correctly knowing all the answers. Similarly, the belief that Our Lady is without sin is not the same as the belief that she was made perfect, for only God is perfect. It merely means that she does not share that imperfection men, thanks to the grace of Our Lord. After all, inanimate matter--rocks, trees, a stream, etc--is also without sin, yet nobody claims that it is "perfect" in the fullest sense of the word. A Perfect being must also be sinless, but sinlessness alone does not suffice for perfection.