Discrimination comes in many forms, and for many reasons - usually, stupid ones. As societies mature, bigotries become less acceptable and those targeted treated as equals, though not always so. Sadly, some biases never go away. Has the attitude towards non-whites in the US today really changed from the days when the KKK operated openly?
When I was a child in the 1970s, it was still acceptable for public school teachers (not just mine, but elsewhere) to "discourage" left handedness in children with corporal punishment (read: beatings) to force children to change hands. Disparagement came in other forms - claims of "being satanic", "hamfisted", "awkward" and others. And just look at the language: many words for "uncoordinated" come from the word for left (e.g. gauche, sinister, etc.). It's comparable to the insult in the word "hysteria", the outdated and sexist mentality that all women are neurotic.
I never received encouragement as a left hander on a first hand basis. My sense of normalcy came second hand, watching athletes or people on TV using the left hand naturally. My parents shared the same outdated mentality as my teachers, so it was present 24/7. Fortunately, I eventually (in grade four) encountered teachers who were enlightened and didn't do that. They were the first people I met in my life who didn't.
Physical abuse didn't occur often (mainly because it was illegal for teachers to hit students), but it wasn't just the physical assaults that displayed discrimination against myself or other naturally left handed children. Teachers would deliberately use passive-aggressive means against children, such as forcing left handed children to sit or work in certain locations. For example, I was often placed to the right of right handed students at tables made for two. Our elbows would constantly collide, and my teachers would blame me. Any attempts to respond to the false blame would be met with, "Then write your right hand!" And if I wanted to move to other tables or switch sides with the right handed student, I was not allowed to. It's not just myself, other left handers my age have related similar stories.
Today, left handed children in developed countries don't face such discrimination anymore, even in countries like Japan which were notorious for enforcing right handedness in the past. But there still are subtle biases throughout society and in the manufacture of products.
Go look at your telephone, and pick up the receiver. Where is the connecting cord? It's on the left side of the housing. If you think that's a benefit for left handed people, trying picking up a pencil and write something. How can a left hander write when the receiver is in the left hand?
I am most definitely not attempting to equate the experience of left handed people with discrimination against gays, ethnic minorities, atheists, women or other groups. What left handers experience today is inconvenience rather than discrimination, but it still exists. I'll have more to say about it again.