Of course the logo can be made bigger or smaller. The answer to this question is more related to the realm of aesthetics than to the realm of possibilities. Of course it can be done. But is it required? Does it help?
The logo designer would like to constrain the size of the logo in context. With relation to a business card, for example, there could be various possibilities when it comes to sizing the logo. The best choice would be something that is visually appealing and more often than not, a large image of the logo, on a business card, for example, would not be aesthetically pleasing. Most clients would want to increase the size of the logo because as human beings, in majority, we assume that if it is big, it will be more visible – which is true – logically – at the same time, as a business-owner or as an individual seeking their brand identity, a large-in-size logo [ in context of course ], might come across [ to the viewer ] as the brand trying too hard – ‘wannabe’.
When the logo is to be printed on a billboard, for example, logically the size of the logo will be larger than when the logo is printed on the business card. Even so, if it is an advertisement, you wouldn’t want the logo to crowd / hog space more than the message of the advertisement itself. There is an exception to this – when you’re simply announcing the presence of your brand in a new geographic spread – and your brand is already well-known internationally – you could simply blow up your logo to 80% the size of the billboard and add a by-line to the effect of, “We’re here.” and be done with it.
How the logo is applied to the medium, would determine the success of the message you, as a business-owner, are trying to convey to the viewer, visitor, potential customer.
So yes, the logo designer CAN make the logo bigger – it needs a flick of the wrist and a couple of clicks to increase the size of a logo in vector format – hopefully without much loss of aesthetics. But when your logo designer hesitates in making the logo bigger, ask him / her why that might be a problem. More often than not, the logo designer’s answer will tell you that they have your best interest in mind. After all, you’re paying them AND they want that logo in their portfolio.