Why Antarctica was never conquered before the advent of the modern men?

Existence

The existence of a Southern Land was postulated by the Greeks, on grounds of symmetry. Aristotle (Meterologica, II, 5) writes:

Now since there must be a region bearing the same relation to the southern pole as the place we live in bears to our pole, it will clearly correspond in the ordering of its winds as well as in other things. So just as we have a north wind here, they must have a corresponding wind from the antarctic.

Settlement

The closest historical episode of settlement in the polar region that I can think of is the Norse settlement of Greenland. The differences are striking.

The Norse were a seafaring, agricultural society. They could rely on a (comparatively, see below) advanced political system to support their expeditions. Settlements in Greenland were supplied with local agriculture and trade, and trees were notably growing in the region for them to build and cook. They remained small, because the climate was nevertheless rigid and there weren't many suitable places were to create settlements. Climate change, alongside the arrival of the Inuit people, determined the failure of their colonization attempts.

On the other hemisphere, the only candidate people we can reasonably think of are:

• Polynesian people
• South African people
• South American people

Of these, only the Polynesian had sufficient seafaring abilities to reach Antarctica in great numbers. Coming from Equatorial and Tropical regions, they were unprepared to settle in the harsh (euphemism) climate of Antarctica. Even though in the Medieval Warm Period the climate could have been milder, it was still a challenge for the Norse in Greenland. The Arctic temperatures in turn are milder than those of the antipodal region, so even if there was discovery, most certainly there has been no colonization.

The South American Yaghan people, used simple canoes to travel between islands. Their adaptation to cold does not seem adequate to face Antarctica's climate. (Compare e.g. to Inuit's clothings).

This rules out any previous settlement.

Discovery

As for the discovery, we must consider that none of these people left written records, so we must rely on oral accounts.

Hui-Te-Rangiora

Polynesian oral history relates that a great explorer, Hui-Te-Rangiora, sailing far south of New Zealand around 650 A.D., discovered a “white land”:

According to traditional accounts the chief Hui-Te-Rangiora, was the first person to discover Antarctica. Leaving Rarotonga in the Cook Islands, he was given directions to reach Aotearoa – New Zealand but he and his crew missed it and carried on until they saw “a white land that was floating.” These white lands are accredited to the great icebergs of Antarctica.

_{from Maori associations with the Antarctic, Turi McFarlane, Canterbury University, 2008}

Te Waka o Tamarereti

Maori oral traditional also tells of the Polynesian explorer Tamarereti who also ventured south to find a “white land”. [...] he was a mortal being albeit the most intrepid of ancient mariners, but mortal nevertheless, suggesting a historical perspective more so than a mythological one. The Maori had observed the Aurora of the far southern regions, when the whole sky seemed to be ablaze at regular intervals. It was thought that a god may have kept his temple there and that the “darting shafts of splendour were signals of his activities.” Because this was a puzzle to the cosmological Maori sages (tohunga), Tamarereti (Reti) announced that he would voyage to the far south and discover the secret of the Aurora. [...] Te Rua o Maahu, a magnificent ocean going canoe was built of Totara and ornamented with plumes of feathers and paua shell. [...] the far south was reached as the tale consists of enormous ice cliffs with towering mountain ranges behind them. The ice cliffs were described as having no footing. The season was said to be suited to observation of the Aurora Australis which was a spectacular blaze of colour and eventually after shortening days the sun disappeared completely their guide the stars alone implying that they crossed the Antarctic Circle.

_ibid.