Parrying requires strength.
Not really. Sword fighting does not require a lot of strength. That is just a myth created by films and videogames.
Consider that most swords weight in the range of 1-1.2 kg. Yes, there are heavier, but those are rarer and usually for specific roles.
In fact, strength is not even one of the most important aspects in sword fighting.
The most important, by far is skill and technique.
The only situation where strength becomes a dominant factor is with heavily armoured opponents, such as wearing maximillian type armour.
Because with this type of armour, there are so few gaps to exploit, that it usually devolves into a grappling match. But in this situation, the sword is mostly used as a lever, to tackle the opponent into the ground.
But, if 2 knights get into this kind of fight, the sword is not the best weapon, but rather the knife, especially one with a strong blade, capable of exploiting narrow gaps in the armour.
The other fact to consider is that in a battle, most of fights between knights would use spears and lances, as these were their main weapons.
But Japanese armour was usually very open, giving greater emphasis to mobility, rather than to protection. So there were many more gaps to exploit, in the case of a sword fight.
Also consider that the primary weapon of a samurai is the bow and arrow, followed by the spear. The sword is just a backup weapon, the last resort in a battle.
Outside of battle, the sword was used as personal protection and a status symbol. But in this situation, the samurai would not be using armour, so skill becomes the primary factor.