You can't just say 'nuh uh' and then not back it up with LITERALLY anything, that's not how this works, we aren't twelve!
Here's my (correct, historically backed) argument and if you don't reply back with anything even sort of cohesive that's a forfeit and I win.
Assuming this is a fair and open fight because otherwise you're just being a dick, which honestly I wouldn't put beyond you.
Mounted troops were still used in some combat roles during the early stages of the 20th century, so thats *very* modern, meaning a single rider might have a saber, pistol, carbine, and lance depending on the period. Ninja doesn't win against gun, no one wins against gun.
Also no one wins against 'charging horse', horses are terrifying.
More points against your fictionalized ninja:
Their job was often to avoid fair fights rather than seek them out.
1. They had much different training focus
◦ A samurai, knight, or cavalryman often spent years training specifically for open combat.
◦ A shinobi's training emphasized stealth, observation, deception, and survival.
◦ Heavy armor and large weapons are advantageous in battle but can hinder stealth, so Shinobi generally favored mobility and concealment. Shuriken aren't making it through platemail. They just aren't.
3. Outnumbered in conventional battles
◦ Large-scale battles reward discipline, armor, formation tactics, and battlefield experience.
◦ Solo espionage skills do not translate into success at the above.
4. Often their success meant avoiding combat
◦ The ideal mission often involved entering and leaving unnoticed. If a ninja ended up fighting heavily armed guards, something had usually gone very wrong. And they died.
For further reading on the subject, see 'Ninja: Unmasking the Myth' Written by leading Japanese warfare historian Stephen Turnbull.
Also Fullmetal Alchemist is better than Naruto by leagues. Stay mad about it.