Scotsmen will say NO. To them and very many kilt wearers the kilt is a kilt, not a skirt. It is a garment of its very own, they say, and exclusively for men. Calling the kilt a skirt is accordingly considered an almost unforgivable insult.

But should you feel insulted then when someone says you are wearing a skirt, or asks you why you are wearing a skirt?
It must depend on how it is said or asked. By far not all calling your kilt a skirt or even a dress have a wish to insult you. Many, not being in a Scottish context, simply don't have the noun kilt on the tip of their tongue.
"Nice skirt!" or "nice dress!" might therefore very well be a praise. And you should react accordingly.

And well, according to all dictionaries I have seen a kilt is defined as a skirt or kind of skirt:

AllWords.com

1. a traditional Scottish garment, usually worn by men, having roughly the same morphology as a wrap-around skirt, with overlapping front aprons and pleated around the sides and back, and usually made of twill woven worsted wool with a tartan pattern.
2. (historical) Any Scottish garment from which the above lies in a direct line of descent, such as the philibeg and the great kilt or belted plaid.
3. a plaid, pleated school uniform skirt sometimes structured as a wrap around, sometimes pleated throughout the entire circumference

American Heritage Dictionary/Answers.com

A knee-length skirt with deep pleats, usually of a tartan wool, worn as part of the dress for men in the Scottish Highlands.
A similar skirt worn by women, girls, and boys.

Cambridge Dictionaries Online

A skirt with many folds, made from tartan cloth and traditionally worn by Scottish men and boys.

DC DictioraryCentral.com

A skirt, usually of tartan cloth worn by men in Scotland, and also by women.

Definitions.net

1. a pleated kneelength tartan skirt worn by Scotsmen in the Highlands or in some military regiments.
2. a skirt modeled on this for women and girls.

Dictionary.com

Any short pleated skirt, especially a tartan wraparound, as that worn by men in the Scottish Highlands,

Merriam-Webster

1. A knee-length pleated skirt usually of tartan worn by men in Scotland and by Scottish regiments in the British armies.
2. A garment that resembles the Scottish kilt.

Oxford Dictionaries

A knee-length skirt of pleated tartan cloth, traditionally worn by men as part of Scottish Highland dress and now also worn by women and girls.

The free Dictionary

1. A knee-length skirt with deep pleats, usually of a tartan wool, worn as part of the dress for men in the Scottish Highlands
2. A similar skirt worn by women, girls, and boys.

Thesaurus

A knee-length pleated tartan skirt worn by men as part of the traditional dress in the Highlands of northern Scotland.
A skirt - a garment hanging from the waist; worn mainly by girls and women.

Urban Dictionary

1. A knee-length wrap skirt with vertical knife pleats on the sides and back made from a tartan woolen cloth and traditionally worn by men of the Scottish Highlands. (Traditional usage)
2. A skirt similar to the traditional Scottish kilt, and may have differing properties such as a solid color, non-tartan patterns, having pleats all around, or varying overall lengths. Generally associated with being worn by men and boys, but is sometimes worn by women and girls. (More common usage)
3. Any other type of skirt sold as a kilt, or a skirt worn by men. (Most liberal interpretation)

Webster's New World College Dictionary

A pleated skirt reaching to the knees, esp., the tartan skirt worn sometimes by men of the Scottish Highlands.

A skirt, it seems, but so what?

A Mercedes-Benz is a car, but far from every car is a Mercedes-Benz.
Women do wear kilts, even if Scots refer to them as being kilted skirts. But look at them. The difference between a man’s and a woman’s kilt is considerably bigger than between his and her jeans, isn't it?