Gothic art is said to originate with the Church of Saint Denis in Paris. Clearly, though, this Church represents only a kind of symbolic beginning, the true origin of the Gothic being impossible to pin down as it developed organically out of the Romanesque. In fact, the movement was so organic that it was only centuries after it replaced Romanesque as the preferred style across Europe (especially in the North and West) that it was even given a name. 16th-century Renaissance artists who sought a return to the more strictly Classical rejected the Gothic as a "barbaric" corruption of the "purity" of more Classical forms. The term "Gothic" is, then, retrospective and pejorative, being a reference to the violent Sack of Rome by the Gothic barbarians.
In one sense, these Renaissance artists were correct. Gothic is a kind of "corruption" of Classical purity and simplicity. The Gothic is, I would argue, a legitimate development of Classical art via the Romanesque. While similar development can be seen in all the artistic media, it's most clearly seen in the two styles' monumental architecture. For instance, let's compare these two arcades, one from the Pantheon in Rome, and one from Notre-Dame de Paris:
Both have columns with bases, shafts, and capitals, supporting an architrave and entablature with similar detailing, atop which sits a cornice. Even though in the former this all supports a pediment and in the latter the structure continues upward, the only significant difference between the two arcades is that in the Gothic example the columns can be skinnier, and in exchange more numerous, as a result of the arches which distribute the weight amongst them. (This is one of the ways in which Gothic architecture is able to feel so light and airy. By splitting the weight up amongst a larger number of thin columns, one prevents the heavy clunkiness of a small number of immense columns.)
Nevertheless, development though it is, it is true the Gothic accumulates and innovates forms which "corrupt" Classical purity. Let's look at a reconstruction of the Parthenon's facade verses that of Cologne Cathedral:
I've chosen the Parthenon specifically because it's of the Doric Order rather than the more ornate Ionic or Corinthian to illustrate my point more forcefully. Even though the proportions of the two buildings are similar, this may be hard to recognize simply because of all the decoration glued onto the Gothic facade. Where Classical architecture was largely content to leave its structure as it was, for the most part adding only what was necessary to hold the roof up in a beautiful and orderly manner, the Gothic feels compelled (almost obsessively) to slap on as much ornamentation as the underlying bones of the structure can hold up.
I said the Renaissance was right to call this development a corruption. The trouble is, the Renaissance was incorrect in rejecting it. What the Gothic did was take the Classical (and true) notions of form (function), beauty (proportion), and truth (honesty of construction), and capitalized on them to create something both imminently Classical. The Gothic "baptizes" the good in pagan art which was attained by human reason, by adding the supernatural, the heavenly, the grace of Christ. Gone is the reticent austerity of Classical architecture, a building can now be a Sacrament of Truth, a material vehicle for the transmission of God's Life to us.
By virtue of the God made Man, things which were formerly unreachable, purely spiritual realities, are now accessible in and through the material world. Wood, stone, and glass are no longer mere tools to hold a roof up, but great mysteries that point to God's participation in the World. Suddenly they contain within them, analogically, hints of Christ's ongoing interaction with us. A wooden beam now calls to mind the Wood on which hung the Savior of the World. A stone, the Rock on (or out of) which Christ builds his Church. Glass, the heroes of our faith, the saintly intercessors, through whom Heaven's Light falls on the faithful. A Church building can become, quite literally, Heaven on Earth: