In short, you appear to be mixing cause and effect; i.e., correlation is not causation.
A higher suicide rate among the LGBT population can mean two things:
1. Being LGBT causes a higher suicide rate
2. Being LGBT is correlated with a higher suicide rate
The first conclusion postulates that the mere state of being LGBT, independent of environmental, social, circumstantial, or other factors, increases suicide risk; in other words, no matter how accepted or ostracized LGBT people are, no matter their upbringing, no matter any other factor, they will always have a higher suicide rate.
The second conclusion, on the other hand, allows for the possibility that some external factor can come into the picture to produce the observed result, and that being LGBT does not innately mean a higher risk for suicide. For example, perhaps LGBT people are relegated to a second-class place in society, with reduced opportunity to find love and having to constantly act in an “unnatural” way in order to be treated fairly. These additional stresses can add up to an increased suicide risk, without which an LGBT person would have a “normal” suicide risk.
By saying “ I think it's clear that it is harmful to be LGBT”, then bringing up suicide rates without mentioning possible confounding factors, it seems you’re drawing conclusion number 1 from above, which, strictly speaking, is too strong of a conclusion to draw given the stated data.
