The reason I question science, is that science is no longer a matter of conducting experiments and generating an outcome, but a matter of having faith in a book of information that someone else has given us, similar to religious texts.
If you were taught from a young age that 2+2=5, you would believe that 2+2=5. However, if someone actually came along with the truth and told you that 2+2 is really equal to 4, you would argue to the death that 2+2=5.
Our brains are programmed just as the processor in your PC. Even if you were to ask your PC a question, it will only give you an answer back that has been programmed into the memory of it.
Thus, we realize today that there is more information that you can be programmed with that defies logic but supports science as you're taught. As an example, going from planet earth to the moon, is said to be a 'scientific fact', however while looking at the facts, you'll see clearly, it's impossible to get through the van Allen radiation belts that are situated between the earth and the moon, as NASA scientist Don
Pettit states, 'We don't have the technology to go to the moon anymore'. And as Neil DeGrasse Tyson, even he makes the mistake in stating that the world is oblate (like a pear) rather than the perfectly round globe we see today in images provided by NASA (admittedly CGI) by NASA's graphic designer, Robert Simmons.
We can have a perfect picture of Saturn, Mars, and Jupiter, why do we not have a clear composited photograph of our own planet today as an oblate object? This is just where you can start to have a seed planted in you that will perhaps grow, and have you question mainstream science. The technology you have at your fingertips today, will not only have you explore the simple question 'Did we go to the moon?' It will teach yourself to always question everything, including the science you've been taught.
The most important thing, is to just keep asking the right questions.