No privacy. Everyone would come to know with whom you are talking or on whom you are taking more interest. So even if you don't tell your well-wishers about your crush, it won't be so difficult for them to find it out.
Relationships would break easily. Some people dislike their partners talking to someone else when they are readily available. So, it would be disappointing for them to see their loved ones chatting with the other person.
Ignoring would be difficult. Most of the times, when we don't wish like talking to the person whom we see as irritating, we come up with an excuse of being busy or in a meeting right right now. So these excuses won't work anymore.
Stalking would be easy. There are people in your friend list who keep the track of your online activities. They like each and every picture you upload and comment on it. Introduction of such feature will work in the advantage of such folks.
Boss would keep an eye on you. If you are chatting at the workplace, and your boss sees you online, then things can really turn out to be scary. You can't even pop up with excuse of talking at home.
More heartbreaks. Wasn't that blue ticks enough that this feature came up to crush the hearts of one-sided lovers. There is no painful thing than seeing your crush ignoring your message to talk to someone else.