I have never thought of "secret" friends...
But the keyword is, undoubtedly, "secret". A "secret" means that there is a good reason to keep someone or something entirely to oneself, which includes lying. Lying is lack, if not total absence of trust; therefore, lack of respect.
To me, love is not enough for keeping a healthy relationship.
Respect and trust is.
I think that it is easier to forgive or/and understand cheating or having an affair (depending on the context) than to forgive lying. Unfortunately, cheating and lying happen simultaneously and for the one who is being lied to it is hard to say what hurts more.
Coming back to cheating. I cannot really think of any other reason for "secrets" than cheating but since it is suggested it seems like the most obvious if not logical explanation.
If hypothetically there are reasons for any other "secret" connections, the danger is the same - the secret alone is the way of creating bondage, heightened emotions and dramatic circumstances. No wonder, "secrets" bring two people closer together and if these two people happen to be of opposite sex, sex is more likely to occur even if it was not on the agenda in the first place. (Maybe it is likely to occur if people are of the same sex, I don't know).
There are very good reasons for "secrets".
People may not be aware of them at the beginning.
If people want to cheat in the first place then "a secret" is only a technique.
I might be entirely wrong, but I am of the opinion that "the secrets" will eventually backfire on the one who lies. We make our choices, we are responsible for them and the consequences and we learn. To cheat or not to cheat? To lie or not to lie the next time?