NodeJS FileSystem Json Read and Write only one works

for a school project I have to rewrite a Json Object using node fs. I wrote a module and if I use deleteCity or addCity on their own, they work perfectly fine. But when I call both after another only one works. In my JSON File there is one array with 10 objects. In my main javascript file I require my module and call upon addCity and deleteCity functions.

//Modules
const fs = require("fs");

//Variablen
const citiesPath = "./cities.json";

//Funktionen
const deleteCity = (name) => {
    fs.readFile(citiesPath, "utf-8", (err, jstring) => {
        if (err) {
            console.log(err);
        }
            try {
                let data = JSON.parse(jstring);
                for (let i = 0; i < data.length; i++) {
                    if (data[i].Name == name) {
                        data.splice(i, 1);
                    }
                }
                fs.writeFile(citiesPath, JSON.stringify(data, null, 2), (err) => {
                    if (err) {
                        console.log(err);
                    }
                });
            } catch (error) {
                console.log(error);
        }
    });
};

const addCity = (obj) => {
    fs.readFile(citiesPath, "utf-8", (err, jstring) => {
        if (err) {
            console.log(err);
        } 
            try {
                let data = JSON.parse(jstring);
                data.push(obj);
                fs.writeFile(citiesPath, JSON.stringify(data, null, 2), (err) => {
                    if (err) {
                        console.log(err);
                    }
                });
            } catch (error) {
                console.log(error);
        }
    });
};

const showCity = () => {
    fs.readFile(citiesPath, "utf-8", (err, jstring) => {
        if (err) {
            console.log(err);
        } 
            try {
                let data = JSON.parse(jstring);
                console.log(data);
            } catch (error) {
                    console.log(error);
        }
    });
};


//Exporte
module.exports = {
    deleteCity,
    addCity,
    showCity
};