"Public good" is a term of art in economics which means a good is both non-excludable (it is impractical to control who benefits from it) and non-rivalrous (one person benefiting does not prevent others from also benefiting).
Roads are clearly rivalrous and while it's often impractical to prevent non-payers from entering a toll road, one can certainly record them and met penalties after the fact to discourage it.
You’re both right. Roads can be an impure public good.
At low traffic loading, they are not rivalrous and can be modelled as a public good. At high traffic loading they become rivalrous and thus closer to a common-pool resource.
If roads are made excludable, they resemble a club or even private group.
Roads are clearly rivalrous and while it's often impractical to prevent non-payers from entering a toll road, one can certainly record them and met penalties after the fact to discourage it.
So no, roads are not a public good.