The line-item veto is a power granted to some executives (most Governors in the US have it, for example) to veto not entire pieces of legislation, but specific pieces. This makes the veto, and hence the executive, much more powerful. I'll give you some arguments for an against, and you can decide which ones you find worth expanding on.
In the US, whether or not the line-item veto is Constitutional hinges upon how we read the Presentment Clause:
"Every Bill which shall have passed the House of Representatives and the Senate, shall, before it become a Law, be presented to the President of the United States: If he approve he shall sign it, but if not he shall return it, with his Objections to that House in which it shall have originated, who shall enter the Objections at large on their Journal, and proceed to reconsider it."
If we interpret "Bill" to mean the entire document presented to the President, then the line-item veto is obviously un-Constitutional. But if we interpret "Bill" to mean any proposed change in laws, then the line-item veto could be Constitutional, since each line-item is itself a change in laws. In 1998 the Supreme Court ruled in favor of the former reading, banning the line-item veto. Before that point, Bill Clinton had exercised it over 80 times.
So, by law, a Constitutional Amendment (or a reversal by the Supreme Court) would be required to restore the line-item veto. But aside from the reading of the Constitution, there are also moral arguments we could make about whether or not the line-item veto should exist.
How powerful do we want the executive to be, compared to the legislature? The ability to veto entire bills already grants significant power to the executive, and the ability to veto only parts of bills would greatly expand that power. While the main uses of the line-item veto in practice involved removing minor additions to budget bills, there's nothing in principle from stopping an executive with the line-item veto from fundamentally changing the character of a piece of legislation by removing certain parts of it. For example, I've linked an example of some extensive rewrites that the Governor of Wyoming made to the state budget by heavy use of the line-item veto. I agree with most of the changes---but I'm not sure he should have had the authority to make them.
On the other hand, without the line-item veto, the legislature can add riders to bills that have nothing to do with the original intent of the bill, and then the executive is forced to either pass the riders or veto the entire bill. A number of very questionable pieces of legislation have been written into budgets; a veto of the budget could trigger a government shutdown, just as the failure to vote on a budget triggered a shutdown in 2013.
For example, "indefinite detention" provisions were included in the 2014 defense budget, which President Obama would almost certainly have line-item vetoed if he could have. But he didn't want to veto the entire defense budget, so he signed it. (Interesting thought: He could actually have tried, citing the Fourth Amendment; basically he'd be saying "this rider is un-Constitutional, so I don't need the line-item veto; it should not be there." Then the Supreme Court would have to rule on whether the provision itself was Constitutional.)
One could also argue that the executive should have more power, because voters appear to be much more engaged in electing the President than they do in electing Congress, and therefore the President may be a better reflection of the true values and interests of the voting population. The fact that the President is elected by state instead of by district also means that the votes might be more representative (you can't gerrymander a state). On those grounds, giving more power to the executive (within reason; we're talking about a line-item veto, not a dictatorship) could actually be considered more democratic.