An anti-'shipper is a Daria story created with the specific purpose of discrediting a romantic pairing between characters by showing perceived flaws and insurmountable hurdles that the relationship might come up against. Generally speaking, any fanfic describing a failing relationship is an anti-'shipper, but the term is most commonly used to refer to the Daria/Tom and Daria/Trent pairings due to their importance in certain sectors of the fandom.
Anti-'Shipping in Daria Canon
While being the ones to set many of the most important ships up in the first place, the creators of Daria also worked toward sinking them in the show itself. "Jane's Addition" simultaneously set up the Jane/Tom relationship and brought a close to Daria's infatuation with Trent. "Dye! Dye! My Darling" ended Tom and Jane's time together and set up Daria/Tom, which would later come to a halt in Is It College Yet?; IICY? also ended Kevin/Brittany. Both The Daria Diaries and The Daria Database would imply Jodie and Mack's relationship was hollow and unsatisfying, and up until "Sappy Anniversary" the series would regularly imply, for laughs, that Helen and Jake's marriage was failing.
Glenn Eichler has stated outright in an interview with Kara Wild that Daria and Trent were not meant for each other, and there has been a great deal of fan speculation that one of the reasons Tom was introduced was to quell rumors concerning Daria and Jane becoming a couple. He also raised the issue that Helen and Jake may - or may not - be the type of couple that seperates once the kids have moved out.
Anti-'Shipping in Daria Fanworks
While many anti-'shipper fics are created based on irreconcilable differences between the characters in question, some other are crafted in reaction to specific pairings being simply overused.