There’re no rules; but there’re generalizations. You may omit it if:
1. A common noun is used in its wildest sense.
Ex. Man is mortal.
2. The noun is a name for a material.
Ex. Silver is a precious metal.
3.1. Before a proper noun. An article may be placed before it to turn it into a common noun.
Ex. Einstein is a great scientist.
Ex. He is the Einstein of the family
Ex. English is a complicated language.
3.2. Before name of a holiday, day, month, year, illness, title, meal & street.
Ex. New Year’s day falls on Sunday.
Ex. Corner of 2nd St. & Main Ave.
Ex. Mumps; Measles.
Ex. Chancellor Helmut Kohl of W. Germany.
Ex. We had lunch.
Note: There’re many exceptions to this.
Ex. The US; The UK; The Dead Sea; The Yangzi.
4. The noun is an abstract or uncountable noun used in a general sense. If the noun is being qualified, it may have the article.
Ex. Honesty is the best policy.
Ex. Apple is good for you.
Ex. The wisdom of this man is unsurpassed.
5. Before a title used in apposition to a proper name or as the complement of a sentence.
Ex. Conrad Black became Lord Black in England.
Ex. Professor Iqbal.
6. In some phrases consisting of a transitive verb followed by its object.
Ex. To set foot; To take offence.
7. In some phrases consisting of a preposition followed by its object.
Ex. At home; To prison; To bed.
Please note this is the item you mentioned in your examples.
Remember they are many exceptions to the above. Their use is idiomatic. Like Feebs11 I’m not aware of any theory behind this.