At the 2017 Conservative Political Action Conference (CPAC), the event's organizer Dan Schneider denounced the alt-right, describing it as a "left-wing fascist group."

“There is a sinister organization that is trying to warp its way into our ranks,” said Dan Schneider, the executive director of the American Conservative Union, which runs CPAC. “We must not be deceived by [a] hateful, left-wing fascist group.”

Over a few confusing minutes, Schneider argued that the “alt-right,” a term coined then popularized by the National Policy Institute’s Richard Spencer, was philosophically left-wing because it departed from his definition of conservatism, in which “the individual” is sovereign.

“They hate the Constitution. They hate free markets. They hate pluralism,” Schneider said. “Fascists tend to want big government control.”

There are a few points I want to make to rebuke this claim that fascism and the alt-right are "leftist" ideologies:

1. Left-wing ideologies usually advocate egalitarianism, in which the people are equal socially and economically. Class structures and other forms of social stratification are eliminated or at least mitigated to some extent to promote equality. Racism, sexism, and other forms of bigotry are usually combated (although left-wingers can be bigots like anyone else). Fascism is inherently anti-egalitarian: certain racial, ethnic, national, or religious groups are deemed superior to all others; age and gender roles in society are emphasized; and a stratified class structure is maintained (although class conflict is neutralized through "class collaboration"). Right-wing ideologies usually advocate traditional values, social order, and hierarchical models of society, so fascism would fit in there.

2. Fascism is not inherently anti-capitalist. Fascists prefer a "third position" between Marxist socialism and laissez-faire capitalism. They want a mixed economy with both public and private ownership of the means of production, with elements of both free enterprise and state planning.

3. "Alt-right" is more of a catch-all term for various groups associated with the right-wing. But these groups, and the alt-right in general, can be considered right-wing because of the proliferation of anti-egalitarian views by people considered alt-right: racial supremacism and racial nationalism, anti-feminism, and religious intolerance (particularly by Christians against Muslims and - to a lesser extent - Jews). As far as I'm aware, no alt-right figures or groups are opposed to capitalism. They might oppose neoliberalism and free trade (on the grounds of economic nationalism), but overall they consider capitalism to be a better system than socialism. If anything they might adhere to the "third position" economic views of traditional fascists.

4. In regards to whether the alt-right is a "conservative" movement or not, it should be noted that the alt-right has drawn influence from paleoconservatives such as Pat Buchanan and Samuel T. Francis. Buchanan and Francis both oppose multiculturalism and high levels of immigration (both legal and illegal), and both support economic nationalism and elements of white nationalism (at the very least they believe the United States is a fundamentally European nation whose identity is being threatened by non-European immigrants). Buchanan has even promoted "white genocide" theories: his 2001 book The Death of the West claimed that Western civilization would "die out" because Westerners would be outbred by Asians, Africans, and Latin Americans. All in all, the alt-right is at least partly descended from paleoconservatism, which is considered a right-wing ideology.

TL;DR: Left-wingers advocate egalitarianism. Fascism and the alt-right are anti-egalitarian. Fascists and alt-righters are not opposed to capitalism, just some elements of it. The alt-right is descended from paleoconservatism, a right-wing ideology, so it makes sense to place it on the right.