Slight necro of this thread, but I read in another post that you had asked a number of questions about European economic history that hadn't been answered, so I thought I'd give it a go. I'll add sources and figures to this answer once I return to my office on Monday, but until then here's an explanation from memory.
To understand why agriculture remained such an important sector of the Danish economy even after industrialisation, you have to go back to the late 19th century. The second industrial revolution reached the Scandinavian countries in earnest beginning around 1850. The European periphery responded to the rapidly increasing demand for raw materials created by the growth of industry in Britain and continental Europe. Thus the first stage of industrialisation across Scandinavia focused on the mechanisation of existing patterns of production. Sweden and Norway both developed their mining and lumber industries. Denmark, on the other hand, is relatively lacking in extractive raw materials. There were no sizeable forests, nor substantial bodies of ore or coal upon which to base such industries. Being a flat, open country relatively well suited to farming, domestic capital instead went into the agricultural sector – largely because it offered the greatest return on investment. Agricultural production increased further in response to increased demand, created by growing urbanisation in Germany and Britain – the chief markets for Danish produce.
Over the decades leading up to the turn of the century, grain prices fell as the development of steam and communications technology began to allow large quantities of cheap American and Asian grain and rice into Europe. This prompted a second phase of development in Danish agriculture, which turned from grain production to animal husbandry. Access to cheap American grain and fodder also allowed Danish farms to maintain a very high animals to land ratio, increasing efficiency of production.
Both the mechanisation of production, as well as the transfer from grain production to animal husbandry was greatly helped by the creation of agricultural cooperatives. As representatives of the leading economic sector, the Danish farming lobby held extensive political power through the 19th century. Farmers used their political power in part to support a very high degree of economic liberalism. Between 1870 and 1914 Denmark was perhaps the most liberal economic society in the western world, having very little government regulation of economic activity. Farmers used this economic freedom to create cooperatives, pooling their capital and market power. The cooperatives owned and ran large parts of the infrastructure supporting the agricultural sector - grain and fodder importing firms, farming supply companies, slaughterhouses, dairies and even banks and insurance companies. – in effect creating private regulation in place of government regulation, as it became very difficult for independent farmers to operate outside of the cooperative system. The cooperatives also facilitated increasing levels of mechanization through the pooling of resources, allowing individual farmers relatively easy access to modern farming equipment, as well as modern industrialised dairies and slaughterhouses.
The government also supported the agricultural sector in numerous ways. From the 1840s Denmark rapidly developed an extensive publicly commissioned railway network, with numerous local stations so that agricultural produce could be exported easily and cheaply. Following crises in the interwar period, the Danish government also sought to negotiate bilateral trade agreements securing continued access to foreign markets for Danish agricultural produce. Although Danish industrial production and service sectors also grew through this period, agricultural produce by 1900 made up 89% of all Danish exports by value.
The early and rapid mechanisation and specialisation in Danish agriculture during the latter half of the 19th century was highly successful. Between 1870 and 1913 GDP per Capita growth rates stood at 1.57%, above the Western European average (1.33%), and well above Britain (1.01%). Altogether, Danish agriculture had by 1900 achieved a reputation for high quality produce at relatively low prices - a reputation that has largely been maintained to this day.
edit: Sources