We've all heard the arguments.
The transgender rights side demands that transgender individuals be able to use the restroom that they are most comfortable with. They state that gender is a social construct that we identify with, separate from biological sex, and if an individual identifies with a gender that does not match their sex they should be allowed to use the restroom of the corresponding gender.
The opposition claims that allowing transgender people to use a bathroom different from the gender they were born with poses a security risk: pedophiles and sex offenders could claim to be transgender just to use the opposite sex's restroom. However, there is a major problem with this claim: transgender people using the bathroom they are comfortable with is not the problem. Perverts, pedophiles, and other sex offenders are. They have been sneaking into bathrooms for as long as we have had them and will continue to do so no matter what restroom transgender people use. The simple facts are that sex offenders exist, and that barring transgender people from using the restroom they are comfortable with is discrimination. You cannot discriminate against transgender people just because perverts exist.
One of the most infamous cases of discriminating against a population for fear of possible criminal activity was the internment of Japanese Americans during World War II. For those who don't know (or choose not to remember), the American government chose to force 120,000 Japanese Americans to relocate to internment camps during WW2 because of fears that some of them may sympathize with the Japanese. These people were forced to move despite many of them being American citizens and were held for at least two and a half years - and many of the American people supported it. Nowadays, we look at the unjust discrimination against the Japanese American population with disgust and shame. We can clearly see that discriminating against the many for fear of the few was wrong; so why are people so willing to discriminate against transgender peoples for fear of sex offenders?
There are an estimated 700,000 transgender people in the United States (almost six times as many Japanese Americans that were relocated). Obama's Bathroom Directive prevents such a national outrage as the discrimination against the very, very many from happening in our schools, where children are bullied every day for things even more trivial than their gender. It allows students to comfortably use the bathroom that they identify with. What it does not allow is for cisgender perverts to use the restroom of the opposite gender. Sex offenders should be dealt with as they always have been and shown that "taking advantage" of the the transgender situation is not acceptable. That is the solution to the problem. Not discrimination.