In Othello, what does Iago mean by "Tis the curse of service preferment goes by letter and affection and not by old gradation"?
Iago is saying that the curse of military service is that preferment, or promotion, does not go by seniority or experience but by favoritism. In Shakespeare's time it was easy for an aristocratic young man to get commissioned as an officer, but for a commoner without connections it was nearly impossible, regardless of how brave he was or how much actual fighting he had participated in. Iago is jealous of Cassio because he, like Desdemona, is a member of the upper class. Iago takes it for granted that Cassio got the promotion he himself wanted because of Cassio's connections.
“Certes,” says he [Othello],
“I have already chose my officer.”
And what was he?
Forsooth, a great arithmetician,
One Michael Cassio, a Florentine
A fellow almost damn'd in a fair wife
That never set a squadron in the field,
Nor the division of a battle knows
More than a spinster; unless the bookish theoric,
Where in the toga'd consuls can propose
As masterly as he; mere prattle without practice,
Is all his soldiership.
Cassio obviously has a much better education than Iago, although Iago has much more military experience. So Othello was not merely guided in his choice of Cassio as his lieutenant by Cassio's, polished manners, social status and connections. Othello may have felt that he himself possessed all the military experience that was required and that he could use a man who was well educated in military science and tactics. Iago seems to be something like a master-sergeant in the American army who can never rise to the level of a commissioned officer because of his lack of higher education. Cassio, on the other hand, seems like a first or second lieutenant, the lowest of the commissioned officers in the American army, but almost certain to keep getting promoted with advancing age, experience, and proper behavior. When Iago gets him drunk and disorderly, it is a terrible blow to Cassio's pride and reputation as well as a black mark on his record and a grave threat to his future career.
It is understandable that Iaqo should be jealous and envious of Cassio, but Iago loses viewer sympathy because he seems eaten up with jealousy and envy of everybody. There are plenty of people like this to be met with today, and many of them can be quite spiteful.