I've been tying for 40 years and tie most of my flies, but buy plenty. Also, nothing beats bumming a fly from a fishing buddy.
I have a lot of reasons for buying flies, here are some:
1. There are some flies I just don't like tying - like quill bodies. I buy all my red quills these days.
2. Professional tiers generally tie better than me and sometimes I have more confidence with a better tied fly.
3. Local flies. For shops that tie their own you can get some great local flies and support the local fly shop. local flies make great, inexpensive souveniers.
4. Get a collection of reference flies. For patterns originated by a certain tier or shop it sometimes pays to buy the original. I like a knock-down dun from the Baxter House, a biot sulphur or electric caddis from Biot, a Shenks's white minnow from Ed Shenk, a Mr Rapidan from Harry Murray etc. Can be either a reference, a piece of history, or just a good fly.
5. Can be cheaper if you need only a few and the fly takes special materials that you don't have.
In addition to buying flies, there is nothing like gifts from your fishing buddies. I have a lot of stories of using flies given to me. Biot gave me a Iso spinner that was my confidence fly last summer that I must have caught 50 trout on. Once at the Little Lehigh I was confounded by a midge hatch and the late Al Miller gave me a simple brown midge that solved the problem. Part of the fellowship of fly fishing is trading flies. Getting a fly that turns your day around after your buddy has been slaying them while you caught the skunk is a treat (although the price may be be teasing for a season or two) and bumming some flies when you forget your fly box at home or dropped it into the water and watched it float away can save your trip and make some new friends. Of course, you need to give flies out too so the kharmic forces are in balance.