There absolutely is a border crisis, just not the type that the right is claiming there is. For the most part, it roots back to a sudden wild spike upwards in the number of people coming into the country, which causes two big problems:
There's a huge backlog of asylum / deportation cases which means people stay in custody in racist and oppressive overcrowded prisons
We're rate limiting the people coming into the country (see point #1), which means a lot of asylum seekers who are trying to do it legally wind up waiting for months (maybe years now, IDK) on the other side of the Mexican border, basically just living in a big, dangerous, squalid, crime-ridden open-air field with no facilities for life, and no job, no medical care for anyone no matter how young or old, it's fuckin dangerous
Then, add to that that the whole agency in charge of the border police is for the most part made of racist people, and then add overcrowding and shortage of resources, and it's fuckin bad for the people who are winding their way slowly through the system.
Biden is unable to fix the problems, although (aside from the racist police) they do have legislative solutions, because the Republicans block anything he does, even when he tried promising to do some cruel or racist things as a compromise in order to get them to also agree to some badly needed things (mostly, increasing ICE funding so they can at least house the people they have in better conditions, and increasing the number of judges to process cases so people don't wait for a year before their case is heard).
And, any time he tries to do anything about it, e.g. reducing the rate of people allowed to come across the border or increasing funding for ICE, everyone on the left as far as I can tell thinks he's just being cruel on purpose for no reason and gets really mad at him.