As far as I know, it is impossible to find out who blocked you on Twitter unless you happen to find it out by chance. My Twitter account MyInnerRandi that I started November 5th, 2009, had my find three blockings. At least two of them I can reasonably pinpoint.
First was AgeOfAutism. IT being a vehicle for J.B. Handley I found I was blocked November 11th, which I tweeted that day 7:41AM EST. Looking back, two tweets might have been the cause:
November 5th, 10:42AM
"Whatever your opinion, you really don't want J.B. Handley and Andrew Wakefield to defend it."
November 6th, 12:48PM EST
"@AgeofAutism Preliminary investigations had found no link. The possibility is still investigated. Misrepresent statements is insinuating."
[I believe it was about the case of Desiree Jennings]
After that there were a few more generic tweets containing, directly or indirectly, my opinion on vaccination and autism.
The next I found to have blocked me was GenRescue, a organization more or less headed by Jennifer McCarthy, J.B. Handley and Jim Carrey.
November 11th 7:42PM EST I tweeted:
"Read school's report on my son's autism. Nothing new, still confronting. These are moments it's hard to remain calm towards @genrescue c.s."
["Read" should been been spelled "Reading"]
Less than 10 hours later, I tweeted I was blocked. They are efficient towards those who disagree with them. Remarkable for people that complain about like treatment by the medical profession.
In both cases my remarks apparently were so harsh and vile, they could read no more. Reading especially the Age Of Autism site, I wonder why.
Another block that I cannot pinpoint so precise comes from an Irish homeopath. I can imagine the reason although I never addressed him directly.
Generation Rescue and Age Of Autism have no qualms about blocking opponents. A mildly critical comment by me on Age Of Autism never got through. If they can't ignore a person, often because someone has above average exposure (they place high value in publicity, not in evidence), they use insinuating language and false claims.
I, an asperger with an autistic son, the type of people they claim to be representing, can safely be ignored. Meanwhile, the psychological make-up of these people is a puzzle to me.