For one, If you need to be tested for an std, you probably are eligible to donate. ( re the questions they ask about your sexual history before you donate)
second, What if you do have it and they don't catch it, not only you won't know you have it yet(because if they find it they will let you know, partially for your health, and so you don't donate again), but then you have probably spread it to someone or even more than one person. Then that person/people won't know they have it, and they could spread it to others and it goes on and on.
third because where i donate it specifically says not to on the information they have to give you.
"You may not donate if you:
have cold or flu symptoms on the day of donation or do not feel well
have ever used a needle to take nonprescription drugs
had hepatitis after the age of 11
ever had a positive Hepatitis B or C test
are at risk of catching or spreading the AIDS virus."
I could not find where it mentions not to donate just to be tested for an std, it it does say it somewhere.