(I'm a native Spanish speaker.)
Why the apparent change of gender?
arte can be either feminine or masculine in any sense, per the DPD:
Este sustantivo, que era femenino en latín, puede usarse en ambos géneros, teniendo en cuenta que, en el español actual, cuando va en singular, lo normal es usarlo en masculino […] y, cuando va en plural, lo normal es usarlo en femenino.
The reason no doubt is related to the fact that arte takes el as its singular article no matter what, so after enough uses of el arte(fem.) contrasted with las artes(fem.), some people started reinterpreting the singular as el arte(masc.). Words that began with /a/ underwent some interesting changes especially during the period in which the rules for when you use feminine article el were in flux.
After a period of confusion, arte settled with the sort of uncountable-ish use in masculine, and when used in a more skill-based sense, being feminine. Because the former is used normally in singular and the latter more often in feminine, the association of masculine-in-singular and feminine-in-plural came about, but it's not strict or universal: el arte posmoderno es interesante mientras los artes vanguardista y moderno me aburren; poder escribir poesía es un(a) arte literaria. So basically, the confusion continues today, permitting use in either gender.
Las palabras agua, águila, arte, hacha, entre otras, son femeninas y por eso se dice las aguas, las águilas, las artes y las hachas pero estas palabras tienen además la particularidad de comenzar con "a" tónica.
Para evitar la cacofonía de la doble a tónica en el singular se usa "el" así: el agua, el águila, el arte y el hacha.
Según la RAE:
Por razones de fonética histórica, este tipo de palabras seleccionan en singular la forma el del artículo, en lugar de la forma femenina normal la. Esta regla solo opera cuando el artículo antecede inmediatamente al sustantivo, de ahí que digamos el agua, el área, el hacha; pero si entre el artículo y el sustantivo se interpone otra palabra, la regla queda sin efecto, de ahí que digamos la misma agua, la extensa área, la afilada hacha. - See more at: http://www.rae.es/consultas/el-agua-esta-agua-mucha-agua#sthash.p5aFUB75.dpuf
De igual forma aplica para los artículos indefinidos un y una
También la RAE dice lo siguiente específicamente sobre la palabra "arte":
No obstante, con el sentido preciso de ‘conjunto de normas y principios para hacer bien algo’, es normalmente femenino, incluso en singular, y así se habla de arte amatoria, arte cisoria, arte métrica o arte poética. En el español actual, si se usa en femenino singular, debe llevar la forma el del artículo, por ser palabra que comienza por /a/ tónica (→ el, 2.1): el arte poética, no la arte poética. http://buscon.rae.es/dpd/?key=arte&origen=REDPD
Nótese que dice "es normalmente femenino" porque en su twitter aclaran
I was going to add this as a comment because what I'm about to write doesn't necessarily give you the "why," but instead, the "what" about some of the differences between "el/la arte" and "los/las artes." I think guifa does the best job of that and DGaleano adds some important points. My answer adds on to what guifa has said regarding the subtle nuances between "arte" when treated as masculine and "arte" when treated as feminine, both in singular form and in plural. If translations over at Reverso provide any reliable, useful lessons with regard to this, it would be the following:
The use of "el" + "arte" often refers to "art" in general and is often used without a definite article in English. This applies even when adjectives are combined with it. Some examples:
¿Qué es el arte? (What is art?)
Las cosas que hago por el arte. (The things I do for art.)
Algunas personas no entienden el arte. (Some people do not understand art.)
And this applies even when a descriptive adjective is added to it:
el arte callejero (street art)
el arte contemporáneo (contemporary art)
el arte primitivo (primitive art)
el arte abstracto (abstract art)
el arte surrealista (surrealist art)
For more, see: el arte.
Sometimes "el" + "arte" will refer to a singular type of art. For example:
el arte marcial (the martial art)
The indefinite article with this term is used similarly. For example:
La danza folklórica conocida como "Tinku" comenzó como un arte marcial.
(The folk dance known as "Tinku" began as a martial art.)
But "martial arts" would be "las artes marciales."
I also visited the Wikipedia article on "Art" and a key point made in it (and something guifa alludes to in his answer) is this:
Until the 17th century, art referred to any skill or mastery and was not differentiated from crafts or sciences.
Having said that, in English, conceptually, there exists a huge divide between what we would consider the "fine arts" and what we would consider (again, from Wikipedia):
acquired skills in general, such as the decorative or applied arts.
However, in English, when we say "the arts," we are usually referring to art created for aesthetics or beauty (e.g., painting, sculpture, photography), but not practical or functional purposes (e.g., pottery). Keep in mind that the lines between these two distinct types of art blur a bit. For example, photography could be created for aesthetic purposes, commercial purposes, or both. The same is true for pottery, architecture, and other works of this nature. Regardless, I highly doubt the average English speaker would make any distinctions between these different types of arts — the aesthetic and the practical. Anything remotely artistic might be referred to as "the arts" and I'd say fewer than 25% of the English-speaking population would even be aware of the distinction between "fine arts" and "applied arts."
As for the Spanish language, I don't know if, in common usage, distinctions are made between "fine arts" and "practical arts." But I can tell you that terminology exists to distinguish between them (at least according to what I found via Reverso).* For example:
fine arts = las bellas artes
practical arts = artes prácticas
However, "a fine art" would simply be "un arte," and "the fine art" would be "el fino arte." On the other hand, "a practical art" would be "un arte práctica" (cacophony rule in play here). You can also use "las artes aplicadas" for "practical arts."
As you can see, both are grammatically feminine and this applies to several other types of art that, in English, we tend to use only in their plural form. For example:
the applied arts (las artes aplicadas)
the decorative arts (las artes decorativas)
the performing arts (las artes escénicas)
the visual arts (las artes visuales)
Just another observation I made through Reverso. Here are some examples:
the primitive arts = las artes primitivas
primitive art = el arte primitivo
the contemporary arts = las artes contemporáneas
contemporary art = el arte contemporáneo
Namely it is this:
los artes = gear
las artes = art
For examples, see:
The examples of "la arte" that I saw were so few that I must assume that adherence to rules related to "cacofonía" (see DGaleano's answer) were simply incorrect and not to be used. But it goes beyond that because I don't believe I saw any instances of "una arte" either.
So, as I mentioned earlier, this does not answer why there are differences, but what the differences are. Nevertheless, I felt the content of my answer was closely enough related to be added here rather than break it off into a separate post. If anyone disagrees, I can recreate it, Q&A style. HTH.