While Leary certainly deserves much of the credit for popularizing psychedelics, he was far from the only one who did so.
The interest in psychedelics was already widespread before he got involved, with Wasson's report in the enormously popular Life magazine about the use of the sacred mushroom, with Huxley's influential Doors of Perception, and before that many exposes on the psychedelic experiences of hashish. Ken Kesey's Merry Pranksters were also great popularizers of LSD, with their Acid Tests, as were the Beatles, the Grateful Dead and other musicians and artists (we seem to forget that, but they were hugely influential).
Leary has been charged with encouraging irresponsible use of LSD, but that's not really true either, from everything I've been able to find on him. He always urged the responsible, careful use of LSD, with a clear understanding of its risks, and also made clear it wasn't for everyone. His ideal set and setting was in small groups, in quiet settings, in safe spaces and in nature.
The kind of use he advocated was actually quite similar to what the ideal set and setting is today, though of course back in the early days they didn't know as much about it as we do now, so it wasn't always ideal. They were still experimenting and researching, which was really what Leary wanted to focus on himself, but he didn't want to limit its use to just research and medical settings, as he saw great potential in psychedelics catalyzing positive societal transformation, which was really part of what at the same time scared the powers that be, who wanted to keep the status quo where they were in control and in power.
The ones who encouraged reckless, irresponsible use of LSD (though they hardly ever get even a fraction of the blame Leary does) were really the Merry Pranksters, who would do things like to give people massive doses of LSD without their knowledge and try to freak them out, and had thousands of people participating in their Acid Tests. It's a testament to how safe these substances were that many more people didn't have lasting negative damage despite such less than ideal circumstances.
Much more to blame for the eventual illegalization of LSD and other psychedelics were the mainstream media, politicians, and the general public who were whipped up in to a frenzy by what they saw in the media and heard from politicians. Both the mainstream media and politicians loved to focus on the minority of bad experiences people had sensationalize the hell out of them, facts be damned. They really bear the overwhelming brunt of the blame, in my eyes.
There were, of course, some horrific events like the Manson murders, which were blamed by the media on LSD. Art Linkletter's daughter committed suicide, and he blamed it on LSD. The media ate all this up and hyped it up, so no wonder people were scared, even though events like these were in the very tiny minority compared to the millions upon millions of times that LSD had been used by that time.
In to this sort of hysteria Leary stepped in and thumbed his nose at authority and said stuff that upset the powers that be, but really he was more of a convenient and willing scapegoat, who loved to be in the limelight and loved to play the role of the rebel, guru, pied-piper of youth, and the media and politicians lapped it up.
The underlying thing this all revolved around, and which so upset people in power and the general public was the youth culture, the counterculture, and the anti-war movement. All of these were tied up together with psychedelics and cannabis, which were opening the eyes of the youth to what they saw as injustices and also potential ways of doing things differently and better (such as dropping out of the rat race and trying alternative ways of living on farms, in nature, or in communes, or getting involved in the nascent environmental movement, or getting involved in the peace movemenent) which all seemed crazy to the mainstream.
Revolution was in the air at the time, and to the people who preferred the status quo (and who happened to be in power) that had to be stopped, so outlawing psychedelics, cannabis, and other drugs used by minorities (who also seemed to be on the verge of insurrection) seemed to be a good way to get control back.
And it seemed to work, at least partially. Protests died down, the youth stopped using psychedelics and started using speed, coke, and heroin (still not sure exactly why myself.. perhaps it was the media, or maybe they were just bored with psychedelics, which were no longer trendy and seemed to be more of a thing of the past, or maybe they were just burnt out), quit the communes, got jobs on Wall St, and voted for Reagan.
I'm still scratching my head about the U-Turn a lot of the youth from the 60's wound up taking in the 70's and 80's.. perhaps the opposition from the dominant culture and the lure of money and a safe, secure life was too great.
Anyway, sorry for straying from the topic of Leary himself, but I think this all ties together and it's hard to make sense of it without knowing how many of these pieces fit together. There's much more to say about this too. I recommend the book Acid Dreams for a good introduction.