The legal definition of highway is any public right of way available for vehicular travel. For example, in NC:
(13) Highway. The entire width between property or right‑of‑way lines of every way or place of whatever nature, when any part thereof is open to the use of the public as a matter of right for the purposes of vehicular traffic. The terms "highway" and "street" and their cognates are synonymous.
The general population uses two other definitions of highway:
1. A main through road, usually numbered by the state.
2. A high speed fully controlled access freeway.
I've witnessed numerous debates where people misinterpreted things based on different assumptions about the definition of highway. For instance, when a government agency reported on crash statistics on school bus crashes on "highways," many people incorrectly believed that this referred to school bus travel on freeways, and used it as justification to oppose school bus travel on freeways. In fact all the collisions were on normal streets, which are legally highways, mostly at local street intersections near the schools or homes. Some folks refused to believe this, since they oppose having to slow down for the school buses or they oppose long distance busing for integration, and wouldn't stop arguing against freeway use by buses even after it was pointed out that freeways don't have intersections and the freeways were in fact statistically safer.
Bicycling on some highways with wide paved shoulders and few intersections is statistically safer than riding on normal streets. On other highways, a combination of conditions such as poor visibility, lack of lights on the bike in darkness, lack of shoulders, more frequent or complicated intersections, etc. can increase the likelihood of collision, and higher speeds increase the severity of injury. However, these roads are often important for destination-oriented cycling transportation, so the goal should be to improve the roads rather than to discourage cycling on them.