CNN reports, citing sources, two reasons why James Comey may have been fired.

There has been intense speculation about why FBI Director James Comey was suddenly fired by President Trump on Tuesday. 
CNN is reporting, citing a source close to Comey, that his dismissal was prompted by two reasons: “1. Comey never provided the President with any assurance of personal loyalty.  2. The fact that the FBI's investigation into possible Trump team collusion with Russia in the 2016 election was accelerating.” 
On Tuesday, the White House press secretary released a statement that said, “Today, President Donald J. Trump informed FBI Director James Comey that he has been terminated and removed from office.  President Trump acted based on the clear recommendations of both Deputy Attorney General Rod Rosenstein and Attorney General Jeff Sessions.” 
Rosenstein, who began to oversee Comey since Sessions recused himself from the investigation into Russia, reportedly issued a memo criticizing Comey over his words and actions towards Hillary Clinton during the review into her emails. 
However, many critics are dubious about this reasoning including NPR which points out that Trump had not previously indicated displeasure over Comey’s handling of the email investigation.
Meanwhile, Politico is reporting that the president had been thinking about letting Comey go for days, but he finally made the decision, insiders have said, because “He had grown enraged by the Russia investigation...frustrated by his inability to control the mushrooming narrative around Russia.”