A - Thanks for the question!
The most popular answers, and probably the best, give us two reasons:
- John wrote his gospel after the other three Gospel writers wrote their's as well as St. Paul's account in 1 Corinthians. So, the Church already had their accounts and he wanted to emphasize something different in his Gospel - the washing of the apostles' feet.
- John had already given us the discourse on the Bread of Life (John 6) which is the fundamental teaching on the Eucharist in his Gospel. Therefore, there wasn't as much of a "need" for John to give an account of the Last Supper as the synoptic writers gave us. But, he gives us the longest account of what Jesus taught at the Last supper (chs. 13-17).