I applied for an internship here last week for June 2022. I have interned before at 2 tier 2 law firms, have decent publications and moots. Yet they rejected me stating that the slots are filled (lies). They are taking random ones for December who have 0 law firm internships. Where am I going wrong? Ps: that person didn’t have contacts and yet got in. Anyone who faced a similar problem?

First of all, you need to reconsider your attitude towards this entire matter. I am only commenting on that to the extent it is evident from your post. In the space of a short paragraph, not only have you called the firm and the people in it liars, but also made disparaging remarks against your fellow applicants whose quality you are simply not in a position to judge. It also seems that you are considering getting an internship to be your entitlement. Maybe your application revealed a completely different and better attitude, maybe you have written all of these without understanding their implications, maybe you are a very nice, diligent and sincere individual who is just getting frustrated by a rejection. However, for your own sake, I advise that you try to set aside all the negativity from your mind when you are dealing with prospective recruiters and internship providers, or when you write your cover letters, so that it does not affect the tone of your interactions with them and thereby harm your chances. You may consider this as preachy and ignore it entirely, that's your call. I just said it as I saw it.

Always try to show your work by attaching work samples and try to find a team member/partner you would like to work with, and then CC them with you application to the HR.

I feel like they usually send out automated rejections, because I got a rejection from the HR and a proceeding confirmation from the partner, both within the span of a day. I understand the limited opportunities with big firms, so not really unexpected.

Try to stand out and reflect how you'll be a great addition to the team.