I failed the 11+ and was written off at that age. Only two children in my year passed and they went to the grammar school. I've since learned that there weren't many places at the grammar school where I lived. In fact if you look into it the whole 11+ scheme, it was completely flawed.
I was lucky enough to have the chance to go back into education as an adult. I did GCSEs, A Levels, a degree and a post-grad. Not bad for someone who failed the 11+.
In my opinion, the biggest problem with testing children at this age is that you cannot devise a test which can predict the future. Children mature at very different ages, so if you happen to be a mature, hardworking eleven year old you've got it made. If the penny drops later on, you've already been written off.
For me, being written off at age 11 affected me deeply for a long time. I went to an awful secondary modern school and failed at sewing and house craft lessons. I thought for a long time that I wasn't very bright. As I say, I was lucky to have another chance at education as an adult, where I found myself surprised every day that I was doing GCSEs and apparently doing ok. When I got all As in my results I was astonished. I went on to do two A levels in a year and I felt like an imposter at college, who would soon be found out. When my results came and again I had As I almost passed out.