Birmingham and El Paso are about 1,149 miles apart by road. Split the difference and you arrive near Dallas, the city closest to the halfway point between them. That splits the trip almost evenly — about 12 hr 9 min from Birmingham and 11 hr 57 min from El Paso.
Over this distance most people will fly rather than drive the whole way. Dallas still makes a fair, central place for Birmingham and El Paso to converge, splitting the travel instead of asking one side to cross the country.
If Dallas doesn't have what you're after, Austin and Oklahoma City are also close to the midpoint and worth a look — each keeps the drive reasonably balanced between Birmingham and El Paso.
City descriptions adapted from Wikipedia (CC BY-SA); photos via Wikimedia Commons, credited above.