Manchester has a population well north of 2.5 million.
Liverpool has a population of roughly 1.4 million.
Those are the population figures for Greater Manchester and Merseyside respectively. Botched metropolitan counties created in the seventies do not adequately represent the relative sizes of Manchester and Liverpool. For example, it surely can't be right that fairly large and independent Wigan is just a borough of Manchester whilst scouse 'burbs such as Runcorn, Ellesmere Port etc are not Liverpool.
Of course, Manchester is larger than Liverpool but the difference is not nearly as great as many wish to believe. And Liverpool is a major city and not just Bolton with New York crime levels, as is often insinuated on this forum.
Liverpool's largest problem is being located in one of Whitehall's administrative divisions of which it is not considered the centre. Liverpool's the largest city in the country in this predicament and so it suffers more than most places. The fact it's still the size it is and still has the economy it has is a testament to it, quite frankly.
In rail terms, the city has the issue of the Lime Street-bound line not being the only option for most of the city region. There is Chester in the south and Warrington Bank Quay in the east. To a lesser extent, there is also Wigan North Western in the far north east. This is in contrast to the Manchester city region, which, despite having many more notably sized towns in comparision to the area surrounding Liverpool, such as Bolton, Oldham etc, most of these don't have their own lines independent of Manchester. Addtionally, because of the larger number of services per hour to London, Manchester is linked with more intermediate towns, such as Stoke and Milton Keynes, which help justify its services, not to mention Crewe, which is a notable rail head where people will travel to reach both Manchester and Liverpool. However, for Liverpool, they will use London Midland trains from Birmingham, therefore having nothing to do with Liverpool-London flows.
Regardless, the primary reason Liverpool's not currently being given a spur is because of a lack of paths. Remember, Network Rail's original proposal was for a West Coast only line from London to Scotland with branches to Birmingham, Manchester & Liverpool. Because Whitehall wanted Leeds served, Liverpool got bumped off. As a result, the whole area is not getting as good a service as it could/dare I say 'should'. Not only is central Liverpool itself getting a far slower service compared to Manchester (and even Preston) but Chester for the southerly end of the city region will not be on HS2 at all and Warrington is only going to get a single train per hour instead of the two it could get if it were to be associated with Liverpool. So it's not at all unreasonable for people in this part of the country to not be happy about the current proposals and aspire to obtain a better deal.