Because Christ's church continues to the present day and passes to Peter's successors. If Jesus had intended the church to be dismantled after Peter died, he would have said so.
So there’s nothing Biblical about apostolic succession... Thanks!
And of course, those schismatic Roman Catholics once again show their hypocrisy about “apostolic succession” when in fact it continues with the Eastern Orthodox Church, from which they split. RCC is no more “apostolic succession” (itself a non-Biblical requirement of being “a true Church”) than Lutheranism or Methodism.