It exposes your relationship to criticism
In real life, people judge who we are dating or married to. This is amplified when you post each other online because now everyone, including strangers, have an opinion about your relationship.
You can't be sure that everyone who sees you two is truly happy for you. A random comment like 'I didn't expect you two to be a pair' can completely change how you see your relationship.
People will easily notice when you're having issues
Changes in your relationship will be exposed to everyone, which is another reason not to post your relationship.
If you've been posting each other every day but now you've suddenly deleted everything, people will notice that. This is a problem because you will feel like you've unintentionally given people access to your private issues.
It adds unnecessary pressure to your relationship
Posting your private life online can also take away the authenticity from your relationship. If you go somewhere with your bae you will start trying to get that perfect picture and striking caption for Instagram and that pressure doesn't allow you to enjoy quality time together.
You might also subconsciously start pressuring your partner to dress or behave a certain way because the online world is watching. This kind of pressure can be very unhealthy for your relationship.