Imagine you have a friend who roleplays in Second Life. There are all kinds of emoting macros there to supplement the textual channel they use to weave their stories.
Now put that person on the stage. "This has so few options, I can't do anything except stand here and talk!"
That would be obviously ridiculous, right?
The situation is the same in D&D (any D&D), but it's much less obvious because we don't spend our entire lifetime learning to interact with the salient objects of D&D's "space", so our natural intuitions about the flexibility of real bodies in space seem to often get lost in the mess of codified options.
But that's just the intuition pump. Let's look at the rules.
No, a fighter has more options than just "I attack"
Is a fighter limited to standing and saying "I attack"? No more than a wizard's options in the second or third round are just standing there and saying "I cast magic missile."
The basic actions
There are several possible actions in combat that are already codified. Let's get those out of the way, because the codified actions are super-distracting from the real point but need to be mentioned because they're trivially true alternatives to the Attack action and need to be here for completeness: running, dodging, helping an ally, hiding (it's not just for rogues!), disengaging from melee, readying a reaction, trying to spot something hidden, and interacting with an entire world of possible objects that might be nearby.
Yes, a lot of the codified actions might seem irrelevant to a fighter — but only if you prejudice the fighter's position by assuming that they will always be standing toe-to-toe with an enemy, every round, every combat. Being busy crossing swords with a foe does tend to limit your options, especially when you've pre-limited them to a set list of choices, so unless making the fighter look bad is the point of the exercise that's an invalid assumption.
Even if a fighter is a dedicated front-line soldier, getting to and controlling the front line is more complex than just attacking every round, and the available actions are just Lego pieces available to build larger tactics from. A fighter that isn't choosing to be a front-line soldier has the durability to be more dynamic and can pull off damage-risking things squishier characters can't — a fighter is wasted on a monotonous "I attack" every round!
All the world's a stage, even combat
Just like that friend standing on the theatre stage at a loss for what to do, someone who has the idea that the only things their fighter can do are fully described by the basic actions is blinkered by familiar habits. Breaking out of them is superficially trivial — just do something else — but in practice very hard. The more someone is steeped in the concepts of efficient action economy use and optimal tactics, the more their thinking will focus on the codified options even when confronted with an improvisational game system. What feels like freedom for one person can feel like a burden to another. Fortunately 5e recognises that combat improvisation isn't for everyone — there are other classes to choose, with more codified options.
Fifth edition is explicitly bringing D&D back to its improvisational roleplaying roots, where the codified combat options were just that — things players commonly had their PCs attempt to do, slowly codified into specific, repeatable rules from the players improvising their actions and the DM(s) improvising the resolution mechanics. Codified actions are just a way to add a bit of consistency to the most commonly-used actions. They're not a menu of the only actions possible.
Improvisation isn't just possible, it's the rule
This refocusing on improvisation isn't harped on in 5e so far, since it isn't necessary for a group to improvise in combat if they don't all want to, but improvising is a normal, explicit rule now, as explicated in D&D Basic Rules v0.1 with a player-facing sidebar on page 72 and its matching DM-facing sidebar on page 74. Improvising something is not provided as an action — that would merely confuse the point of saying "improvising is possible" (and besides, it's up to the DM's improvisation what kind of action, if any, it is), but it is a rule. It's always been possible, but making it an explicit rule means that players can rely on it to make sure DMs don't limit them to just the list of actions. That doesn't mean DMs can't houserule improvisation out of their game, of course, just that they have to communicate that limitation clearly, if they want to play that kind of game instead of the default.
Given that you can always improvise (and it's backed by rule authority in 5e), the reality is that every option a fighter has in a more rigidly-defined system is available. Think of a codified combat option in another game. Now attempt it with the fighter just by saying you do. That's how 5e works.
"I flip the table in their faces."
"Okay, that's Strength versus their Dexterity to see how explosively fast you flip it and if they get out of the way. Oooh, three failed."
"I trip the orc."
"Cool, okay. Strength versus Strength."
"Do I get advantage or anything?"
"Nah, you've just got a sword. A staff or a chain or something would get advantage, but not a sword."
"I trip the centaur."
"Seriously? I suppose Conan the Buff has a chance even if it's got four legs... Anyway, yeah, Strength versus Strength just like last time, but you have disadvantage."
"I feint with my rapier and stop short, trying to unbalance my foe and open their defense."
"Hm, how about Dexterity versus Wisdom? If you make it, it'll count as Helping yourself on your next attack or your next round, whichever comes first."
"Okay. Wait, what are the Helping rules... Oh, that's just Advantage. Sure. But no need to make it complicated, just say it gives Advantage."
If you can think of something, you can try it. Leap off of tables and try to get your falling weight behind your sword for extra damage. Throw your cloak at their face. Unleash a screaming battle cry to shake their morale. Growl out a demand that they surrender or die as you hack away with the normal combat actions — just because it's an Intimidation attempt doesn't mean you have to look for a combat action to let you do it in combat, it's just talking!
Your friend is wrong
So your friend is right in a way. The fighter's options could be limited to just standing there and saying "I attack" if you're only looking at the list of combat actions as a menu of possibilities. There's very little in the way of real alternatives when you're toe-to-toe with a foe, given that limitation. But there is no reason you should accept that premise in a discussion of fighters in 5e, because 5e doesn't.
Your friend is wrong in the larger system that 5e provides. Combat isn't a special "world" in 5e, where the only things you can do are these N choices and all the normal flexibility of roleplaying is taken away with the flip of the initiative light switch. Combat is just an extension of the freeform part of the game, with a few options nailed down to make sure each group and player has a bit of consistency in the middle of the big Venn diagram of unlimited possibilities.