eBay (NASDAQ:EBAY) is interested in spinning off PayPal, its rapidly growing payments unit, according to The Information. Activist investor Carl Icahn, who owns roughly 2.5% of the e-commerce giant, has repeatedly advocated just such a spinoff.

PayPal accounted for 41% of eBay's net revenue in 2013. The business's revenue rose 19% year over year to $6.63 billion. By comparison, eBay's marketplace business, which accounts for 52% of its top line, only grew 12%. That gap widened in the last quarter, when revenue surged 20% at PayPal, but only 9% at for marketplace.

Source: Wikimedia Commons.

At first glance, spinning off PayPal doesn't make any sense -- why should eBay divest its fastest-growing business unit? Yet by digging a little deeper, we can find three simple reasons to support this move.

1. eBay's toxic reputation could poison PayPal
eBay has suffered huge setbacks this year. The company asked 145 million users to change their marketplace passwords in May after a massive data breach.

Although the breach did not affect PayPal or credit card records, it exposed users' email addresses, encrypted passwords, home addresses, birth dates, and other sensitive information. eBay's response was widely criticized, since it waited over three months to inform the public of the breach, then failed to inform users by email to change their passwords after the news broke.

Earlier this month, eBay's site crashed for the 10th time in 2014, infuriating buyers and sellers who demanded compensation for lost transactions. The outage occurred shortly before eBay raised several seller fees for users in the U.K., once again demonstrating the company's lack of PR timing.

In this context, it makes sense for PayPal -- a payment service that relies heavily on top-notch security and stability -- to distance itself from the significant troubles that have tarnished eBay's reputation.

2. The "bank" of PayPal
If PayPal is spun off and taken public, it would get its own board of directors that could focus on the company's growth without worrying about eBay's bottom line.

According to Icahn's open letter to eBay shareholders earlier this year, an independent board would give PayPal the "opportunity to expand its product offerings to include check writing, direct deposits, interest on PayPal balances, and other financial conveniences that consumers expect."

PayPal originally offered interest-bearing money market accounts, but dropped them in 2011 "due to market conditions." In 2000, those accounts offered a whopping 5.56% annual return, but by 2009 the return had plunged to 0.23% due to the global financial crisis. Since the average rates for a one-year CD in the U.S. still hover near 1%, PayPal could win new users by bringing back interest-bearing accounts. However, eBay might object to that plan due to the short-term impact on the company's net income, which only rose 6% last quarter.

Meanwhile, Amazon.com (NASDAQ:AMZN) recently launched Local Register, a card-reading dongle similar to those offered by Square and PayPal. Amazon is offering a promotional rate of 1.75% per swipe until Jan. 1, 2016, and 2.5% afterward. That undercuts Square and PayPal's respective rates of 2.75% and 2.7%. PayPal might need to lower its rate to defend its market share in a timely manner -- another development to which eBay might object.

Amazon Local Register. Source: Amazon.

3. What's good for PayPal is good for eBay
Icahn's original plan only called for a 20% spinoff of PayPal in an IPO. By selling 20% of its stake in PayPal upon the public offering, eBay would definitely get a nice infusion of cash.

But that initial payday would only be the beginning of PayPal's contributions to eBay. The two companies would appeal to different investors -- conservative investors could stick with eBay, while those itching for growth could buy PayPal. Meanwhile, previous arrangements between PayPal and eBay could be set in stone prior to the spinoff.

If PayPal is liberated to pursue higher growth outside of eBay through new financial features and third-party partnerships, its soaring market cap will boost eBay's value, which would remain the newly independent company's main stakeholder.

PayPal could also use its own stock to acquire smaller competitors, such as privately held Square or Stripe. This means eBay would not need to make big acquisitions, like its recent $800 million purchase of Braintree, to help PayPal grow.

A Foolish final word
Spinning off eBay would be a gutsy move for eBay. But it would be the right play -- it would protect PayPal from eBay's recent controversies, allow it to independently grow its market share without worrying about eBay's bottom line, and could attract new growth investors who would not have otherwise invested in eBay's sluggish stock.