According to Hinduism, and limit it to the factual question of why women are prohibited from going. In any case, the reason for this custom is that Ayyappa is a Brahmachari, so while he was on Earth he took a vow not to associate with women who are fertile, and that custom is maintained in the temple.
1. We cannot find any scriptural evidence for Denial of entry to fertile women. We can ponder over why fertile women want entry into temple. Since a devotee cannot break rules, It is certain that people (atheist women) just want to break the rules made by ancients. If they are so eager to get darshan of Lord Ayyapa they can do it before fertility or after fertility.
2. Before visiting Shabarimala every devotee has to take up vratham (penance) for 41 days and should stay away from alcohol, smoking, non-vegetarian food and all other tamasic things including sex, cutting body hair, shaving and even trimming the nails and should not sleep on bed. They are expected to bath twice in a day and visit the local temples regularly and only wear plain black or blue colored traditional clothing during this time.
3. Since women are considered to be the source of sexual energy, a nitya brahmachari deity has put certain restrictions on female devotees.
4. It's silly to assume that Shabarimala Temple Trust is being misogynistic, because they are preventing 'sex and sensuality' from their premise and not women as kanya (before a woman becomes fertile) and post-menopause (after 60) woman are free to enter the temple and worship.
5. A more liberal and political correct view might be that it intended to ensure that women are not put through the difficulty of traversing the mountain under rigorous conditions and their comfort and safety too could be an area of concern on a pilgrimage like this.