Senator Dianne Feinstein is frequently exasperating. The Democratic senator from California is one day ultra-liberal, in the lead in calling for gun reform. The next she is ultra-conservative, one of the staunchest defenders of the embattled National Security Agency.

The senator's contradictory nature was on show for all to see on Tuesday, when she delivered an extraordinary speech from the Senate floor. It amounted to the biggest and most public rift between Congress and the spy community since the 9/11 attacks. Ms Feinstein, who chairs the Senate intelligence committee, which has oversight of America's myriad spy agencies, accused the CIA of breaking into the committee's computers. It is an extremely serious charge: a breach of the constitution, the executive branch tampering with the elected branch. She described it as "a defining moment for the oversight of our intelligence community".

She is on strong ground. The row dates back to the CIA's programme of torture in the aftermath of 9/11. The CIA and the Bush administration, which presided over the programme, preferred to describe it euphemistically as "enhanced interrogation techniques" but torture it was. Members of the Senate and House intelligence committee only learned about it late, in 2006. A year later the New York Times revealed that the CIA had destroyed videotapes of these early interrogations.

After Barack Obama became president in 2009 and Ms Feinstein became head of the intelligence committee, she started an exhaustive inquiry into the torture, and this is at the centre of the current rift. She claims that the CIA, headed by John Brennan, recently conducted searches of the committee's computers. Mr Brennan, in response, denied that the CIA had hacked into the Senate computers.

It is right that Ms Feinstein should raise this. It is a huge issue, one that at the very least will see calls for Mr Brennan's resignation. Her pursuit of the CIA is the fulfilment of her role as chair of the intelligence committee. It is what she should be doing, the monitoring of the spy agencies.

The exasperation with Ms Feinstein is that she directs her sense of outrage only at the CIA. It seems restricted to issues that impact on her. She is outraged when the CIA allegedly hacked into her committee's computers. She is upset over the alleged intrusion into the privacy of her own staff. And yet this is the same senator who could not empathise with Americans upset at the revelations in the Snowden documents of millions of citizens whose personal data has been accessed by the NSA. It is the same senator who could not share American anger over the revelation of the co-operation in surveillance of the giant tech companies, whether wittingly or unwittingly.

Ms Feinstein not only failed to investigate the NSA with a smidgen of the aggression she has shown towards the CIA but has gone out of her way to be the NSA's most prominent defender. The day after Edward Snowden revealed himself as a whistleblower last June, she was among the first to brand him a traitor. In the face of revelation after revelation, she praised the professionalism of the NSA. She defended mass data collection as a necessity, arguing that the NSA had to have access to the whole "haystack" to find the one needle, the terrorist. All this dismayed many of her Democratic supporters in liberal California and elsewhere in the US. She proposed a bill supposedly aimed at NSA reform, but it was a spoiler, one that in fact would have done little to curb the agency's powers. The one time she wobbled was in the autumn after the disclosure of US spying on German chancellor Angela Merkel. But this proved to be only brief.

It is about time Ms Feinstein used her powers as the democratically elected head of the intelligence committee to question the NSA with the same vigour – or even a small part of it – that she is displaying towards the CIA. That would, indeed, be a defining moment for the oversight of the US intelligence community: all of it.