Let me count the ways (note that these are all features FurBuy DOES have):
(Note: When I say Gallery Sites I mean sites like FA, InkBunny, Weasyl, SoFurry, etc.)

• Bids on Gallery Sites are not legally binding contracts, therefore you have no legal recourse against fraudulent bidders or violations of contract
• Fielding bids is very confusing both for the seller and the bidders, esp with no decent notification system
• Speaking of no decent notification system, users don't receive e-mail from Gallery Sites when there's an important message - most folks these days get their e-mail anytime/anywhere on their phones
• Gallery Site users do not have to provide full contact information when creating an account and are therefore not responsible legal parties
• Gallery Sites have no facilities for forcing maintenance of account status and communications to ensure users are legitimate and active
• Gallery Site journals have zero posterity - they can be deleted at any time without notice by admins or by the poster like the auction never happened (i.e. you will have no record of bids, abuse, etc.)
• Gallery Site comments have zero posterity - they can be deleted/hidden at any time without notice by admins or the poster or by the submission/journal owner (i.e. you will have no record of bids, abuse, etc.)
• Gallery Sites have no policies or terms of service regarding sales and auctions to help protect buyers and sellers and set standards for how business gets done
• Admins and moderators on Gallery Sites have no impetus nor responsibility to mediate or assist in working out issues between you and another party to remediate problems
• There are no systems in place on Gallery Sites to prevent or deal with shill bidding, spite bidding or bid shielding (anyone can have any number of unauthenticated accounts and abuse them to bid against you and jack up their prices - i.e. sockpuppeting)
• There's no bidding system on Gallery Sites, hence no Proxy Bidding to help you out (helps both the buyer and the seller)
• There's no automated, safe, fair ending time system on Gallery Sites to close auctions at the right moment
• Gallery Sites do not have any auction listings systems, making it very hard to find things to bid on or even to find more auctions by the same seller!
• Search engines are (usually) barred from indexing Gallery Sites, which means your auctions will never be searchable using Google, Yahoo, Bing, etc.
• There's a logical fallacy that everyone uses Gallery Sites and watches the artists they like and hence 100% of their bidders would see auction posts on Gallery Sites - this is NOT true at all. People go to Gallery Sites to social network and view galleries not buy things. If you post an auction on a site where people are looking to spend money and then post a journal with a link to that site then you've not only folded in your fans and followers but also getting the attention of the people who genuinely DO have money to spend as well and maybe even getting new watchers!
• Lack of accountability and feedback: after a successful (or unsuccessful) dealing there is no way to report or note that things went good/bad and no rating system for buyers and sellers
• No security systems: Gallery Sites are not at all geared to deal with the security and safety concerns that are unique to sales and especially auctions sites, such as automated systems to find potential fraud users, shill bidders, sockpuppets, etc.
• Not web2.0: Most Gallery Sites don't have any integration with outside sites and 3rd party systems at all and are not likely to ever add such features, so how is this helping you reach a larger audience?
• Banhammers: In the last few years a growing number of legitimate members of furry fandom who buy/sell/trade fursuits, artwork, comics and etc. have come under personal attacks by Gallery Site admins and been banned from the site - do you want such personal conflicts to effect who can and cannot do business with you, or would you rather they only be judged by their track record in dealing with sales and purchases effectively?
• There are now so many Gallery Sites out there today, do you really want to have to cross-post to all of them to get word out about your auction? How do you effectively handle bidding across all those sites?
• Gallery Sites are not auction sites and are therefore missing a set of rich features designed to make auctioning easier, safer and more fun while being a targeted, specific experience centered around your sales and auctioning needs

Did we miss any? Comment and let us know what you think!

The bottom line is simple: Gallery Sites are not auction sites. So why try to make them something they're not? Using an auction site is easier (less headaches in the long run!), safer (lots of policies and security systems in place to protect you) and more specific to what you're trying to do (get your auctions found by people with money and get real, valid bids on them). Why manage your own auction when someone else is offering to manage it for you for free?

(Update: Made minor edits and corrections 2017-1-15)