The reason that all wines are not vegan or even vegetarian-friendly has to do with how the wine is clarified and a process called 'fining'. All young wines are hazy and contain tiny molecules such as proteins, tartrates, tannins and phenolics. These are all natural, and in no way harmful. However, most people tend to like their wines to be clear.
Traditionally the most commonly used fining agents were casein (a protein found in milk), albumin (egg whites), gelatin (animal protein) and isinglass (fish bladder protein). They are not additives to the wine, as they are filtered out along with the haze molecules.
Fining with casein and albumin is usually acceptable by most vegetarians but all four are off limits for vegans because tiny traces of the fining agent may be absorbed into the wine during the fining process. Vegan wines are fining with clay-based products such as Bentonite or activated charcoal. Some producers allow their wines to self-clarify in their own time, and are usually labelled as such, so expect a bit of sediment at the bottom of the glass, or decant!