Imagine if everyone had that 3rd party voting is a waste mentality. The most famous 3rd Party candidate Abraham Lincoln would have never had any support or ever have gotten elected as President.
I like your sentiment, but context is important here. Gotta rewind quite a ways to get there, though.
Slavery had grown into such a heated topic in the 1850s that the two major parties of the time (Democrats and Whigs) were both starting to fracture. In 1852, anti-slave Whigs blocked the renomination of Fillmore (incumbent pres + Whig) for president (instead going with a taller dude than Lincoln called Old Fuss and Feathers in an election they lost to Pierce), and the party itself fully split over the next 2 years. Former Whigs in the north became Republicans, while in the south, they went by Know Nothings (such a good party name).
Democrats had stayed united with Pierce, a northerner with southern sympathies, and were still managing alright. They tried it again with Buchanan, and while they won the 1856 election, he gaffed hard enough on a slavery issue (Dred Scott case) that he basically handed the northern congressional offices to the Republicans in 1858. He became pretty despised, and by 1860, just wanted out of office. Here's where we see the Democrats fall apart.
Pro-slavery radicals in the south (called Fire-Eaters, these guys had such great names) wanted to reopen the slave trade that had been closed for over 50 years. They were fearful of Republicans gaining more power and were beginning to seriously talk about seceding from the Union. The Democratic Convention of 1860 was fiercely contested, with Fire-Eaters eventually walking out and Democrats nominating two candidates, one for the north and one for the south.
So, by the time Lincoln was elected in 1860, Republicans weren't really a third party, at least not in the sense that we see third parties now. They were more like 1 of 4 major parties, as both major parties had split over the past decade. They were also doing well as a party in terms of congressional representation and had a large backing from the start. Plus, on a more negative note, half the country seceded from the Union because he was elected, culminating in the bloodiest war ever fought on our soil, so he's not really the best poster child for third parties :x