Hood was the largest ship built for the Royal Navy in the 20th Century, and, was until recently the largest ship in its history. For much of her life, she was the largest warship in the world. But more than this, she was seen as beautiful, or graceful, in a way that few other ships in the RN were. She was the pride of the RN because she was physically impressive and imposing, less so because she was thought of as the most capable ship in the fleet. It's worth noting, though, that she was never a fleet flagship; she served as the flagship of 1st Battlecruiser Squadron and of Force H, but Home Fleet and Mediterranean Fleet always used battleships as flagships.

Hood was awe-inspiring in her might, in her size, and in her design; Ted Briggs, one of the three survivors of her sinking, described his first encounter with her:

I stood on the beach for some considerable time, drinking in the beauty, grace, and immaculate strength of her. 'Beauty' and 'grace' seem rather ludicrous words to describe a vessel of such size, particularly one whose primary function was for destruction. But I can honestly say I never could, nor indeed can even today, think of more suitable words to describe her.

The look of a ship went a long way with the sailors of the RN, and with the general public, much more than the capabilities of the ship. A simple way to show this is to look at the nicknames the ships received. Nelson and Rodney, both more heavily armed and armoured than Hood, received the disparaging nicknames 'Nelsol' and 'Rodnol', because they resembled tankers in design. Ramillies, equally well-armed and armoured as Hood, was the 'One-funnelled Baa-Ram'. Hood was only ever 'the mighty Hood'.

Hood also, thanks to her cruises with the Battlecruiser Squadron, became a symbol of the might and power of the British Empire. Her first cruise was to Scandinavia, in 1920, but her more famous cruise was the 1923-4 World Cruise. Accompanied by Repulse, she visited the Empire's most important outposts, as well as ports in North and South America. In all these ports, she was a major attraction - at Melbourne, she was visited by 486,000 people in a week. She would visit more countries during her service in later years, especially during her Mediterranean cruises. These cruises turned her from a ship into a symbol; as V. C. Scott O'Connor would describe in his contemporary account of the World Cruise:

In her mass and speed and perfection of armament, the Hood symbolises the valorous determination of war-weary Britain to maintain intact for the good of mankind the far-flung Empire she has built up through the centuries. It is this symbolism that lifts Hood out of the machine and irradiates the great grey hulk with a halo of splendour.

More modern ships like the KGVs had no such chance to gain this symbolism. Completed in the middle of WWII, they were thrown into fighting pretty much from the off. As a result, they never really inserted themselves into public consciousness in the same way Hood did.

From an earlier answer of mine

Flagships can be peculiar things in the twentieth century. Admirals sometimes chose flagships based on habit, others because the ship in questions had better communication equipment. Raymond Spruance preferred heavy cruisers likely for both reasons. Kurita Takeo's flagship before Leyte was the heavy cruiser Atago. He had to transfer his flag to Yamato after the submarine Darter sank her as the IJN taskforce was on its way to Leyte. So flagships are not necessarily the biggest and the baddest ships available. Some though were quite formidable and HMS Hood was one of them/ There were two reasons why HMS Hood earned this particular moniker "pride of the RN."

One, HMS Hood was one of the more prominent ships within the public face of the RN in the interwar period. When launched, she was the largest and fastest capital ships in the world. She held this record well until 1940 with Bismarck's launching. Although Japanese and American battleships too would outshine Hood after Bismarck, the British battlecruiser was still among the most well-known ships in the fleet. One of the major duties of HMS Hood was to serve as the flagship for a number of prestigious assignments such as the head of the Home Fleet's battlecruiser squadron or as flagship of the Mediterranean Feet. This gave her a very high visibility both among the British public and the world. The height of this visibility was arguably the 1923-1924 world tour in which the Hood was the flagship of a RN fleet that visited numerous ports around the globe as a gesture of goodwill. She actually was at the time the largest ship to ever traverse the Panama Canal and a number of ports on the tour were not deep enough to accommodate her draft.

The second reason for HMS Hood's public visibility was that she had little other competition within the interwar RN for the spot. Although she was a battlecruiser, she was better armored in many respects than the Queen Elizabeth-class battleships and faster. The only other capital ships the UK constructed before the "battleship holiday" of the Washington Naval Treaty were the Nelson-class battleships. Although they had 16-inch guns and a decent armor scheme, they did not look like a battleship. They were squat, very slow (top speed was 23 knts), handled poorly, had an asymetiric main armament, and they looked like oilers with their aft-located superstructure. The KGV's were new ships, but were also going through teething troubles. The RN was never quite able to make its quad 14" turrets work as promised and the battleships' design was somewhat compromised by trying to hew towards displacement limits set by the now-abandoned London Treaty. In short, HMS Hood beat its main rivals for being the most modern British battleship partly on aesthetic reasons. Hood's clean lines, rakish bow, and symmetrical superstructure all screamed "battleship" while the Nelsons appeared to be the compromised design they were.

The collapse of the naval limitation treaties did end the battleship holiday, but far too late for the RN. The King George V-class battleships began construction only at the end of the 1930s, so they would only be launched during the war. This meant these new ships had very little time to fix themselves in the public's eye. The advent of airpower and the gradual eclipse of the big guns as the main deciding factor in naval combat meant there was also not much for the King George Vs to do during the war. HMS Prince of Wales had a highly visible career, but as part of failed missions: Hood's attempt to stop the Bismarck where PoW was damaged, and as part of Force Z at Singapore where she was sunk along with HMS Repulse.