First of all, many social media platforms set 13 as the minimum age for users as part of their terms and conditions. If they do this, then it is a breach of GDPR to process data of users who are under this age, according to the UK’s interpretation of that European law.
Secondly, in Europe, under that GDPR data protection legislation, there are a limited number of legal bases for processing personal data. One of these is the consent of the user. But children are only able to give consent to their data being processed if they are at least 13 years old (in the UK, up to 16 in some EU Member States), otherwise they need also to obtain consent from their parent or legal guardian.
Also, many platforms rely on the age given when a new profile is created as the basis of their understanding of a user’s age over subseqeunt years – to filter content, and comply with age-restrictions, such as those applied to advertising for certain products, for purchases or to see adult-only content. So if they start off with a false age, that will remain an issue in future with potentially more significant consequences.