Why does the IRS like to go after low-income people who claim the earned-income tax credit?

Because it yields a high benefit to cost ratio. See The Problem With the IRS Pledge Not to Audit More Earners Under $400,000 by Josh Zumbrun of The WSJ. Excerpts:

"Well, one reason is that the standard calculation of audit rates falls short. They are based on what taxpayers report their income to be. But tax dodgers are by definition underreporting their income.

“People might think it’s very clear who is and who isn’t high net worth,” said Natasha Sarin, a Yale law professor and former Treasury official. “The whole point of tax evasion is people with high net worth are doing a lot of maneuvering and accounting tricks to look like they’re not.”

So while most people who report, say, $300,000 in income are upper-middle-class households with straightforward finances—salaries, a mortgage, children—some are very rich people whose actual income is far above that level but are especially audacious or creative in reporting a lower figure. Those are the people the IRS might very much want to audit.

The problem, simply put, is that reported and actual income are different. Indeed, exempting taxpayers with reported income below a certain threshold can create incentives that widen the gap.  

An unscrupulous person who earned $500,000 might decide it is better to hide $100,000 instead of just a few thousand dollars, because they would then have the reported income of an ordinary person that the IRS has pledged not to pursue too hard."

"Audit rates also present an incomplete picture of how efficiently the IRS allocates enforcement efforts. Why would the IRS ever audit a lower-income taxpayer when auditing a wealthy taxpayer presumably yields more tax? Because from the IRS’s perspective, not all audits require the same effort. It spends a little over six hours on average auditing a taxpayer reporting $25,000 to $200,000 in income, but almost 34 hours on one reporting $500,000 to $5 million. So audit efficiency is best measured by additional revenue per hour of work, rather than audit rate. 

"By this metric, the most effective use of IRS time is going after returns reporting over $5 million in income, which yield an extra $5,000 of tax owed per hour of work. But the second most effective use is auditing households at the opposite end of the scale: low-income people who claim the earned-income tax credit, which yields nearly $3,000 per hour. The IRS has said these audits take little time and have a high rate of funds being recouped because the audits are typically of people seeking a refund, and occur before the refund is issued."

"audits aren’t random. They are triggered by something unusual or a conspicuous mistake. The task facing the IRS: What is the trigger for identifying a taxpayer pretending to be middle class?"

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