What is the opposite word for 若い(わかい, young)?

At the beginning stage of Japanese study, teachers usually would teach vocabularies with their opposite words together such as おおきい⇔ちいさい, あたらしい⇔ふるい, etc. Particularly, students need to be careful about “あつい” and “たかい”. あつい has a variety of meaning such as “hot” and “thick” with corresponding opposite words of “cold” and “thin”. たかい could be “high” and “expensive” with corresponding opposite words of “low” and “cheap”.
 
However, if you use the opposite words without prudence, you might make such funny mistake. Some students probably would say “このジュースはさむいです(The juice is freezing. Here the correct word is 冷たい(つめたい) not さむい)” or “父(ちち)の背(せ)がやすいです(My father is cheap. The correct word is ひくい, not やすい)”.
 
Meanwhile, have you ever thought about the opposite words for 若い? The opposite word should be “old” in common sense and “old” means “古い”. So if you want to say “He is old”, it supposes to be “彼は古い人だ”. But, you’ve just made a horrible mistake because it’s extremely rude to elderly people.
 
Unfortunately, there is no opposite word for 若い. The possible reason might be due to the politeness and prudence of Japanese. People usually avoid direct expression in terms of age. Instead, the negative form a word would be the opposite meaning. Hence, the previous example should be “彼は若くない”. In addition, people usually use “お年寄り” as the respected expression of elderly people.
 
However, why 若い doesn’t have opposite word? I want to know why as well.
 
Enjoy your weekend.