By "strange" I mean 'Is there a reason for this, or is it something we accept as a peculiarity of our universe?'
I see no reason why if magnetic field is in the $+x$ direction and a charge's velocity is in the $+y$ direction, that the force experienced by the charge can't be in either the $+z$ or $-z$ direction, both are perpendicular to $x$ and $y$. The equation for Lorentz force just tells us that it goes in the $+z$ direction, but it seems equally valid that the force would be in the $-z$ direction (I mean there's nothing to distinguish $+z$ from $-z$ anyway, you can turn one into the other by swapping the handedness of your coordinate system). It seems as if the universe is preferentially selecting one direction over the other.
As a practical example, if a current carrying wire is in a magnetic field and it experiences an upward force, why shouldn't it experience a downward force?